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RECONSTRUCTING MACROECONOMICS Structuralist Proposals and Critiques of the Mainstream z lance taylor harvard university press Cambridge, Massachusetts London, England 2004

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Page 1: Reconstructing Macroeconomics: Structuralist Proposals and

RECONSTRUCTINGMACROECONOMICS

Structuralist Proposals and Critiquesof the Mainstream

z

lance taylor

harvard university pressCambridge, Massachusetts

London, England

2004

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Copyright © 2004 by the President and Fellows of Harvard CollegeAll rights reserved

Printed in the United States of America

Library of Congress Cataloging-in-Publication Data

Taylor, LanceReconstructing macroeconomics : structuralist proposals and

critiques of the mainstream / Lance Taylor.p. cm.

Includes bibliographical references and index.ISBN 0-674-01073-6 (alk. paper)

1. Macroeconomics. 2. Macroeconomics—Mathematical models. I. Title.

HB172.5.T393 2003 2003056775339—dc22

Michel
Tampon
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z

Contents

Acknowledgments ix

Introduction 1

chapter one Social Accounts and Social Relations 7

1. A Simple Social Accounting Matrix 72. Implications of the Accounts 93. Disaggregating Effective Demand 134. A More Realistic SAM 195. Stock-Flow Relationships 236. A SAM and Asset Accounts for the United States 267. Further Thoughts 43

chapter two Prices and Distribution 44

1. Classical Macroeconomics 442. Classical Theories of Price and Distribution 463. Neoclassical Cost-Based Prices 524. Hat Calculus, Measuring Productivity Growth,

and Full Employment Equilibrium 545. Markup Pricing in the Product Market 616. Efficiency Wages for Labor 647. New Keynesian Crosses and Methodological Reservations 658. First Looks at Inflation 68

chapter three Money, Interest, and Inflation 79

1. Money and Credit 792. Diverse Interest Theories 873. Interest Rate Cost-Push 884. Real Interest Rate Theory 905. The Ramsey Model 93

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6. Dynamics on a Flying Trapeze 977. The Overlapping Generations Growth Model 1048. Wicksell’s Cumulative Process Inflation Model 1099. More on Inflation Taxes 117

chapter four Effective Demand and Its Real andFinancial Implications 124

1. The Commodity Market 1252. Macro Adjustment via Forced Saving and Real

Balance Effects 1303. Real Balances, Input Substitution, and Money-Wage Cuts 1324. Liquidity Preference and Marginal Efficiency of Capital 1375. Liquidity Preference, Fisher Arbitrage,

and the Liquidity Trap 1396. The System as a Whole 1457. The IS/LM Model 1478. Maynard and Friends on Financial Markets 1529. Financial Markets and Investment 156

10. Consumption and Saving 16111. “Disequilibrium” Macroeconomics 16912. A Structuralist Synopsis 171

chapter five Short-Term Model Closure andLong-Term Growth 173

1. Model “Closures” in the Short Run 1732. Graphical Representations and Supply-Driven Growth 1823. Harrod, Robinson, and Related Stories 1904. More Stable Demand-Determined Growth 194

chapter six Chicago Monetarism, New ClassicalMacroeconomics, and Mainstream Finance 199

1. Methodological Caveats 2002. A Chicago Monetarist Model 2033. A Cleaner Version of Monetarism 2054. New Classical Spins 2075. Dynamics of Government Debt 2116. Ricardian Equivalence 2147. The Business Cycle Conundrum 2188. Cycles from the Supply Side 2199. Optimal Behavior under Risk 222

vi contents

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10. Random Walk, Equity Premium, and theModigliani-Miller Theorem 226

11. More on Modigliani-Miller 22812. The Calculation Debate and Super-Rational Economics 230

chapter seven Effective Demand and theDistributive Curve 232

1. Initial Observations 2322. Inflation, Productivity Growth, and Distribution 2333. Absorbing Productivity Growth 2384. Effects of Expansionary Policy 2435. Financial Extensions 2466. Dynamics of the System 2487. Comparative Dynamics 2498. Open Economy Complications 253

chapter eight Structuralist Finance and Money 258

1. Banking History and Institutions 2582. Endogenous Finance 2613. Endogenous Money via Bank Lending 2654. Money Market Funds and the Level of Interest Rates 2705. Business Debt and Growth in a Post-Keynesian World 2726. New Keynesian Approaches to Financial Markets 278

chapter nine A Genus of Cycles 281

1. Goodwin’s Model 2822. A Structuralist Goodwin Model 2843. Evidence for the United States 2864. A Contractionary Devaluation Cycle 2925. An Inflation Expectations Cycle 2946. Confidence and Multiplier 2977. Minsky on Financial Cycles 2988. Excess Capacity, Corporate Debt Burden,

and a Cold Douche 3039. Final Thoughts 305

chapter ten Exchange Rate Complications 307

1. Accounting Conundrums 3072. Determining Exchange Rates 3133. Asset Prices, Expectations, and Exchange Rates 316

contents vii

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4. Commodity Arbitrage and Purchasing Power Parity 3185. Portfolio Balance 3196. Mundell-Fleming 3287. IS/LM Comparative Statics 3318. UIP and Dynamics 3339. Open Economy Monetarism 337

10. Dornbusch 33911. Other Theories of the Exchange Rate 34112. A Developing Country Debt Cycle 34413. Fencing in the Beast 347

chapter eleven Growth and Development Theories 349

1. New Growth Theories and Say’s Law 3492. Distribution and Growth 3593. Models with Binding Resource or Sectoral

Supply Constraints 3634. Accounting for Growth 3665. Other Perspectives 3706. The Mainstream Policy Response 3727. Where Theory Might Sensibly Go 375

Notes 379

References 405

Index 425

viii contents

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z

Acknowledgments

I took over teaching first-term advanced macroeconomics at the NewSchool from John Eatwell in 1995. The New School economics depart-ment tries to have its courses combine a critical review of mainstreamanalysis with a constructive presentation of more historically and insti-tutionally founded ways of doing economics. The present volume buildsupon Eatwell’s course arrangement in doing just that.

So the main contributors to the material herein were the successive co-horts of New School students who had to suffer through my attempts toput a coherent presentation together. To all of them, my enormous grati-tude, and thanks in particular to Thorsten Block, Christy Caridi, UtePieper, and Matias Vernengo. Many passages of this latest version couldnot have been written without critical inputs from Nelson BarbosaFilho, Per Gunnar Berglund, and Codrina Rada.

Also, thanks to Robert Blecker and Amitava Dutt, who read the wholemanuscript and offered numerous, very helpful suggestions. Ideas builtinto several passages came from Jaime Ros, Duncan Foley, Ron Baiman,Yilmaz Akyuz, and Jan Kregel. Mike Aronson and Elizabeth Gilbert atHarvard University Press and Butch Montes at the Ford Foundationwere quiet but substantial contributors.

My wife Yvonne, daughter and son Signe and Ian, son- and daughter-in-law Joel and Elisabeth, and grandkids Lyla and Imogen were enor-mous supportive, even if the last two didn’t know it. The same goes forall the canine, caprine, feline, equine, porcine, gallinaceous, and (last butmost obnoxious) anserine critters at Black Locust Farm.

ix

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z

Introduction

Macroeconomic frameworks that constrain social and economic actorsand aggregates of their actions are the topic of this book. Diverse schoolsof economists have proposed such schemes. A “structuralist” approach,based on social relations among broad groups of actors, is emphasizedhere.

In the North Atlantic literature, structuralism’s intellectual founda-tions lie within a complex described by labels such as [original, neo-,post-]–[Keynesian, Kaleckian, Ricardian, Marxian] which nonmain-stream economists have adopted; numerous variants exist in developingcountries as well. The fundamental assumption of all these schools isthat an economy’s institutions and distributional relationships across itsproductive sectors and social groups play essential roles in determiningits macro behavior.

The approach adopted here also puts a great deal of emphasis on ac-counting relationships as built into national income and product ac-counts and flows of funds. These relationships constrain the numberspresented in the accounts, which are the fundamental data of macroeco-nomics. Almost needless to say, the conventions used in building macro-level accounts are anything but objectively given. They arose historicallyout of the debates over the Keynesian system, and serve social and politi-cal ends. The accounts are mostly estimated on the basis of data col-lected for other purposes, such as taxation, and are by no means a clearreflection of what is going on in the “real” economy, out there. But theystill define the realm of macroeconomic discourse and have to be ac-cepted and utilized as such.

More important, market-balance restrictions constrain the outcomesof decisions made by economic actors—not every actor can have a tradesurplus with all the others, for example. In practice such statements canbe rephrased in terms of macro-level “sectors” and “institutions” suchas households, nonfinancial business, financial business, government,and the rest of the world (in one familiar scheme). A distinguishing fea-

1

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ture of structuralist theories is that they are constructed directly in termsof aggregates such as household consumption, business investment, totalexports, and so on. Few if any appeals are made to optimizing decisionsallegedly made by individual “agents,” in contrast to most mainstream(especially Anglo-American) macroeconomics.1

In practice, two sorts of accounting restrictions matter—those thatconcern flows (for example, GDP is the sum of payments to labor, pay-ments for indirect taxes, and payments for “surplus” or profits) andthose that cumulate flows into the corresponding stocks (such as the factthat a country’s net foreign assets are the sum over time of its current ac-count surpluses). “Stock-flow consistent” (SFC) macro modeling takesall such restrictions into account.2 They remove many degrees of free-dom from possible configurations of patterns of payments at the macrolevel, making tractable the task of constructing theories to “close” theaccounts into complete models.

Two such tasks are attempted in this book. One is to present a criti-cal review of mainstream macroeconomics from a structuralist perspec-tive. The focus of the critique is on monetarist, new classical, newKeynesian, and recent growth theory models with an effort to studythese contributions from a historical perspective. Various forms of mon-etarism are traced from the eighteenth century, and current monetaristand new classical models are compared (unfavorably) to those of thepost-Wicksellian, pre-Keynesian generation of macroeconomists (KnutWicksell himself, Dennis Robertson, Joseph Schumpeter, the young JohnMaynard Keynes). The new Keynesian vision is contrasted to Keynes’sown in The General Theory of Employment, Interest, and Money from1936, and contemporary growth theories are analyzed against a longbackdrop of thought about questions of structural economic change anddevelopment.

The theories presented as alternatives to the mainstream draw uponwork by Keynes’s immediate disciples (mostly at Cambridge University,including Nicholas Kaldor and Joan Robinson) in the 1950s and 1960s,and contemporary and subsequent scholars including Michal Kalecki,John Hicks, Roy Harrod, Richard Goodwin, Amartya Sen, StephenMarglin, Amitava Dutt, Robert Blecker, Bob Rowthorn, John Eatwell,the American “social structure of accumulation” school (SamuelBowles, David Gordon), other Marxists (Duncan Foley, Anwar Shaikh),and Anglo-American post-Keynesians (Hyman Minsky, Jan Kregel,Wynne Godley, Thomas Palley). As already noted, their emphasis is onsetting out models with clear and complete macro accounting and ex-plicit statements of socioeconomic relationships among the main groupsof actors.3 In the chapters to follow, a fairly complete structuralist mac-

2 introduction

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roeconomics is presented, including output determination, distributiveconflict and inflation, growth, cycles, relationships between the real andfinancial sectors, and open economy complications. Many conclusionsrun counter to standard results, and can be empirically supported.

The discussion draws upon both formal models and historical and in-stitutional considerations. The models are pitched roughly at a first-yeargraduate student level, requiring calculus, matrix algebra, and the rudi-ments of optimal control theory. Keynes’s strictures against applying for-mal probability theory to finance and economics are heeded, so there isscant use of that sort of mathematics. A brief chapter outline follows.

1. Social Accounts and Social Relations. Much of the formal argumentis framed in terms of social accounting matrixes (SAMs) and their associ-ated balance sheets, which are introduced in this chapter. They are usedto illustrate questions of model causality or “closure” (selection amongvarious behavioral restrictions to append to SAM accounting balancesto give an algebraically complete model). For example, given hypothesesabout how diverse groups of economic actors respond to one another(saving decisions by households with different sorts of income flows, dis-tribution of profit flows and investment decisions by nonfinancial andfinancial business, demand choices by the government and rest of theworld, and financial linkages among all these groups), is it more appro-priate to postulate that output is determined by full employment of laborand capital (Say’s Law in its modern guise) or the Keynes-Kalecki princi-ple of effective demand? Besides addressing such analytical questions,the chapter uses SAM-based accounting to display and analyze recentU.S. macro data.

2. Prices and Distribution. This chapter begins with a review of cost-based theories of price determination—classical “prices of production”and neoclassical formulations under perfect and imperfect competition.The next topic is the neoclassical approach to measuring productiv-ity change, which is shown basically to boil down to manipulation ofaccounting identities. Questions are raised for later discussion aboutthe interactions between distribution (measured by the real wage andprofit rates) and labor and capital productivity growth. On the basisof neoclassical production theory, the discussion returns to the issueraised above as to whether macro equilibrium is determined by effec-tive demand or in labor markets according to new classical and/or newKeynesian formulations. A critique of the new Keynesian approach isformulated on Marxist and Austrian grounds. The chapter closes with adiscussion of wage-wage and price-wage distributive conflict theories ofinflation, and their contrasts with monetarist inflation theory.

3. Money, Interest, and Inflation. The discussion begins with a histori-

introduction 3

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cal overview of different positions regarding the effects of money/crediton prices and quantities. It then turns to the diverse roles the interest rateis supposed to play: interest rate cost-push theories of inflation (the“Wright Patman effect”), loanable funds and real interest rate theo-ries (Böhm-Bawerk, Fisher, Ramsey), the overlapping generations (OLG)model and the financing of pension plans, and a Wicksellian monetaristmodel of a “cumulative process” inflation when the market rate of inter-est differs from the “natural rate.” The “inflation tax” central to theWicksell model is at the heart of monetarist inflation models, and thechapter closes with a quick review of the related “Olivera-Tanzi effect”and “tight money paradox” (Sargent-Wallace).

4. Effective Demand and Its Real and Financial Implications. Theprinciple of effective demand is presented in Kaleckian and Keynesianvariants, with discussion of the irrelevance of neoclassical labor demandtheory to Keynes’s model and the theory’s empirical lack of support.The role of income distribution in determining effective demand is ana-lyzed—is demand “wage-led” (the likely developing-country case) or“profit-led” (industrialized countries)? Following a discussion of liquid-ity preference and diverse interpretations of the liquidity trap (Keynesversus Fisher and Krugman), Hicks’s IS/LM model is set out in termsof SFC accounting. Next come discussions of own-rates of interest andtheories of investment demand (Tobin’s q versus post-Keynesian formu-lations), the consumption function and implications, and “disequilib-rium” macroeconomics (Malinvaud). The chapter closes by asking: howwell does Keynes’s own model stand up after almost seventy years? Theanswer is generally positive.

5. Short-Term Model Closure and Long-Term Growth. This chaptermarks a transition between older and more contemporary approaches tomacroeconomics. It starts out with a review of the various closure as-sumptions and “effects” discussed in previous chapters. The next topic ishow these assumptions and effects feed into supply-driven growth mod-els, with investment and growth determined by available saving in Solow(with more discussion of growth accounting) and Marxist specifications,and by investment with an endogenous income distribution for Kaldor.Demand-driven models come next—Harrod, Robinson, and an initialpresentation of a distribution/effective demand model used extensivelyin later chapters. An illustration contrasts the model’s results regardingthe financing of social security schemes with those from an OLG speci-fication.

6. Chicago Monetarism, New Classical Macroeconomics, and Main-stream Finance. The discussion covers the emergence of post–World WarII reactions against Keynes—critical reviews from SFC and effective de-

4 introduction

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mand perspectives of Chicago monetarism (Friedman, Phelps), newclassical macroeconomics (Lucas, Sargent), the role of government debt(“old fiscal conservatives” versus Barro’s “Ricardian equivalence”),complete information finance theory, and the Modigliani-Miller theo-rem.

7. Effective Demand and the Distributive Curve. A complete real-sidestructuralist macro model is constructed in the capacity utilization ver-sus wage-share plane. It is based on an effective demand curve that canbe either wage- or profit-led and a “distributive curve” representing asteady-state (possibly locally stable or unstable) wage share that emergesfrom differential equations for money-wage inflation, money-price infla-tion, and labor productivity growth. Dynamics are shown to dependon interactions between income distribution and productivity growth.The real-side model is then extended to incorporate money and bonds.Finally, an open economy version is set out in which currency devalua-tion can be either expansionary or contractionary with respect to realoutput.

8. Structuralist Finance and Money. The story begins with a historicalreconstruction of the evolution of Anglo-American monetary and finan-cial systems—the roles of “endogenous” money and finance. A model ofendogenous or passive money is presented within an SFC accountingframework (an approach not often taken by post-Keynesians). A post-Keynesian growth model is then constructed, based on an effective de-mand function that can be either “debt-led” or “debt-burdened” and adifferential equation for the growth of business sector debt. The chaptercloses with a quick review of a couple of “asymmetric information”(new Keynesian) approaches to money and finance.

9. A Genus of Cycles. Models of business cycles are presented in atwo-dimensional-phase plane, in which one variable has positive feed-back into itself, and is stabilized by damping from the other—hence the“genus.” Models presented include Goodwin’s predator-prey distribu-tive cycle between labor and capital, an extension based on the Chapter7 macro model with application to the U.S. economy, a cycle basedon contractionary devaluation, destabilizing expectations in the Tobinmonetary growth model, a financial cycle drawing upon the ideas ofMinsky (explicitly rejecting the Modigliani-Miller theorem), and a cycli-cal version of the Chapter 8 model of borrowing by business that cangenerate “overinvestment” of the sort frequently discussed in connectionwith the 2001–2002 U.S. recession.

10. Exchange Rate Complications. Open economy macroeconomics isreviewed with an emphasis on the determination and economy-wide ef-fects of the exchange rate. It is argued that existing models all fail to pro-

introduction 5

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vide exchange rate “fundamentals.” Purchasing power parity (PPP) anduncovered interest rate parity (UIP) exchange rate theories are sketchedfrom this perspective. Next, the familiar portfolio balance model isshown to be treated incorrectly in the literature. When its full SFC ac-counting is respected, it has just two independent equations for assetmarket clearing and so can only determine home and foreign interestrates but not the exchange rate. If asset market equilibria vary smoothlyover time, it follows that the balance of payments equation in theMundell-Fleming model is not independent and cannot set the exchangerate either. The “correct” model is a two-country IS/LM specificationcoupled with exchange rate dynamics. Cyclical properties of a versionincorporating dynamics based on UIP are briefly explored. It is con-trasted with the well-known monetarist and Dornbusch models, whichare also based on correct accounting but make use of PPP and classical asopposed to Keynesian behavioral relationships. Finally, a model of ex-change rate and debt cycles in a developing country context is presented.

11. Growth and Development Theories. Growth and developmenttheories from several different streams over the past two centuries arepresented and contrasted with recently popular endogenous growthmodels and subsequent purported explanations for convergence—orlack of same—of per capita income levels internationally. Drawing onmaterial from earlier chapters, seven lines of thought are explored: fullemployment, savings-driven mainstream growth models; models withfull employment, endogenous distribution, and an independent invest-ment function à la Kaldor; classical models with savings-driven dynam-ics and class-determined distribution; demand-driven growth models asdescribed in Chapters 7 and 9; models built around a binding resource orsectoral output level; development accounting schemes; and specific ef-fects such as economies of scale and externalities. Development policyrecommendations derived from these families of models (including thosepresented in previous chapters and more mainstream formulations) arereviewed and criticized.

As should be clear from these summaries, some topics are covered inseveral different chapters, for example productivity growth in Chapters2, 5, 7, 9, and 11. There is a lot of cross-referencing in the text so thecross-chapter connections should be fairly apparent.

Finally, quite a few distinct algebraic models are presented, each re-quiring its own set of symbols. As a consequence, some symbols changemeaning between sections. Full definitions and redefinitions have (onecan hope) all been provided, but the reader should be on the lookout forthem.

6 introduction

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chapter one

z

Social Accounts andSocial Relations

Another way of putting the points raised in the Introduction is to saythat macroeconomics is framed by social accounting and social rela-tions. The social accounts form a skeleton, and social relations changethe skeleton’s position over real, historical time. Specifying just which re-lations drive the motions is not a trivial task, as subsequent chapters at-test. But the objects that move—the observable phenomena in macro—are mostly the numbers making up the national income and product ac-counts (NIPA), the flow of funds (FOF) accounts, and allied systems. Webegin with those.1

1. A Simple Social Accounting Matrix

Table 1.1 presents a social accounting matrix (or SAM) of the sort pro-moted by two economists from the University of Cambridge—RichardStone and Wynne Godley.2 In all SAMs the two main accounting ruleshave been borrowed from the input-output system and can easily be im-plemented in computer spreadsheet programs: each entry along a rowshould be valued at the same price, and the sums of corresponding rowsand columns should be equal. A good part of macroeconomics com-prises theories about processes that drive these sums toward equality.

As its title suggests, column (1) of the SAM summarizes the costs ofproducing the value of output PX. The symbol X stands for “real” out-put, in practice some index of production gross of intermediate inputswith P as the corresponding price deflator (the more usual notation foroutput is Y, but in this book that symbol is reserved for real or nominalincome flows as discussed in the next paragraph). The costs of producingPX include outlays for intermediate inputs aPX, wages wbX, and profitsπPX. Intermediate uses are assumed to be proportional to gross outputthrough the input-output coefficient a, and employment L is relatedto output X through a similar relationship, L = bX. “The” (average)money-wage rate is w, and π is the share of PX paid out as profits.

7

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Social relations enter the SAM’s structure with the decomposition ofgross output less intermediate costs or “value-added” (1 − a)PX intowage payments and profits. From the “Output costs” column (1) and“Incomes” rows (B) and (C) we have (1 − a)PX = wbX + πPX = Yw +Yπ, where Yw and Yπ stand for wage and profit income flows in nominalterms. They are carried separately on the hypothesis that people who(mostly) get wages behave differently in economic terms from the corpo-rations and real persons who (mostly) share flows of profits, rents, inter-est, dividends, and capital gains.

The extreme case is illustrated in the “Current expenditures” columns(2) and (3) of Table 1.1. All wage income Yw goes to consumption PC(price P, “real” quantity C) and all profit income Yπ is saved as Sπ. Thissort of class distinction fits the facts. Of course, in practice some wage in-come is saved and some profits are consumed (corporate CEOs receiveincome for their labor services, and who besides CEOs, extremely suc-cessful entrepreneurs, or rentiers could support commerce in BeverlyHills or Manhattan’s Upper East Side?), but different savings rates acrossincomes from different sources clearly exist. Besides being empiricallyrelevant, the differential saving hypothesis is a key component of the het-erodox models described in this book. For reasons to be discussed in thisand following chapters, most orthodox or mainstream economists steeraway from class-linked savings rates and even income flows.

So far, we have analyzed a cost-of-production decomposition and in-come-expenditure accounts for wages and profits. The expenditures in-clude “current” outlays only, implying that capital accumulation has tobe treated in another set of accounts. To lead into them, note that row(A) of the SAM sums up the uses of output: PX = aPX + PC + PI,where C and I respectively stand for “final demands” for consumption

8 chapter one

Table 1.1 A small SAM with production, income, expenditure, and flow offunds accounts.

Current expenditures

Outputcosts Wages Profits

Capitalformation Totals

(1) (2) (3) (4) (5)

(A) Output uses aPX PC PI PXIncomes(B) Wages wbX Yw

(C) Profits πPX Yπ

Flows of funds(D) Sπ −PI 0(E) Totals PX Yw Yπ 0

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and investment (gross fixed capital formation plus increases in inven-tories) in real terms.3 The value of investment, PI, is reflected via a mi-nus sign in column (4) from row (A) into row (D) for flows of funds,or changes in assets and liabilities. Despite the fact that there are twogroups of income recipients, only one flow-of-funds row is needed in thepresent setup. With no saving from wage income, its recipients cannotbuild up real or financial claims.

The sign convention is that “sources” of funds (saving plus increasesin liabilities in SAMs which contain detail on financial transactions) arepositive while “uses” (investment plus increases in financial assets) arenegative. In Table 1.1, row (D) says just that. The “net lending” or“financial surplus” of profit recipients is nil (Sπ − PI = 0) because theyput all their newly saved resources into capital formation. It is easy to de-rive this saving-investment “identity” from the costs and uses of produc-tion statements and the income-expenditure balances, or vice versa. Inother words, a balanced set of accounts already puts significant restric-tions on the degrees of freedom of the variables it contains. This mun-dane observation will be of great concern in the chapters that follow.

2. Implications of the Accounts

Some implications of macroeconomic accounting balance are worth ex-ploring in more detail.

First, the SAM in Table 1.1 embodies “circular flow” à la JosephSchumpeter (1934), but with characteristic macroeconomic modifica-tions:

The value of output decomposes into intermediate purchases, thewage bill, and profits, all of which are production costs.

Wage and profit payments generate incomes.Wage incomes generate final consumer demands and intermediate

purchases are also sales. Not all income flows are spent for currentpurposes, however, because profits are saved.

The level of investment is set by enterprises, more or less indepen-dently of current savings flows. Investment goes together with con-sumption and intermediate demands for goods to use up or “real-ize” total output.

The saving-investment identity, Sπ = PI, follows from these flows as atheorem of accounting. Its ramifications are many, but the trunk of thetree is the fact that in capitalist economies the households or divisions ofcorporations which save are not the same as those which invest. In otherwords, there is a potential problem of coordination between different

social accounts and social relations 9

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economic actors. It is made more acute by a second fact: savings and in-vestment flows must be equilibrated through financial markets that havetheir own proper dynamics and are prone to instability.

These particular social relations are the gist of modern macroeconom-ics, as enunciated by John Maynard Keynes and Michal Kalecki in the1930s.4 The roles of different social actors are illustrated by the columnstructure of Table 1.1—firms’ production operations and relations withtheir labor forces dominate column (1), workers’ consumption summa-rizes (2), rentiers’ and corporations’ saving is in (3), and long-term plan-ning by firms interacting with financial markets sets investment in col-umn (4).

Investment behavior is crucial because from the SAM balances, it isclear that even if it is entirely consumed, the wage bill cannot exhaust to-tal product—a corollary of the saving-investment accounting theoremrecognized in 1935 by Kalecki in an article on “The Mechanism of theBusiness Upswing.” The implication is that investment (or some other“injection”) has to be present for demand to be realized. With imperfectcoordination, it is not obvious that the macro system will arrive at a bal-ance between saving and investment with socially desirable properties—for example, “full employment” of the potentially available labor forceand capital stock is not guaranteed. These observations can be illus-trated with a couple of examples.

In the first one, we can “close” the accounts of Table 1.1 with theKeynes-Kalecki principle of effective demand, which asserts that changesin the level of output X are the means by which saving and investmentare brought into equality, with investment being determined indepen-dently of potential savings flows. The algebra is well known and simple.From row (B) and column (2) of the SAM, we have PC = wbX, or C =ωbX with ω = w/P as the real wage. Substituting into row (A) and ma-nipulating gives

XI

a bI

=− −

=1 ω π

where the denominator in the expression after the second equality fol-lows from the cost decomposition in column (1).

Through a multiplier process, output X and employment L = bX aredetermined by investment I and the profit share π. The level of economicactivity will be low, for a low injection I or a high saving “leakage” π.The model is simplistic, but it does illustrate the basic insight that out-put, employment, and saving can adjust to meet the level of effective de-mand as driven by the net effect of offsetting injections and leakages.

10 chapter one

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Much macroeconomic effort after Keynes has been devoted to refutingthis causal scheme, as will be discussed in great detail in later chapters.Full employment can then be guaranteed on the basis of appropriate as-sumptions.

One variant of this alternative vision goes as follows. Let K stand forthe aggregate capital stock, implicitly assumed to be made from the same“stuff” as output X.5 Moreover, X is constructed from available laborL and capital K according to an aggregate production function X =F(L, K), with properties to be described in detail in later chapters. Fur-ther assume that the real wage is set according to the marginal produc-tivity rule ω = ∂F/∂L, and that the rate of profit r = πPX/PK (totalprofits divided by the value of the capital stock at replacement cost) isdetermined by r = ∂F/∂K.

With such input pricing rules, one can construct Walrasian macromodels in which values of ω and r exist such that L and K take on prede-termined, “full employment” levels. If L and/or K shift, moreover, ωand/or r will adjust so that markets for these production inputs con-tinue to clear. Stated somewhat differently, we can put enough mathe-matical restrictions on the production function and other descriptors ofthe macro system to ensure that full employment of labor and capitalcomes about. When that happens, the total saving supply Sπ = πPX =rPK is also determined by the marginal productivity formulas and fullemployment (the level of the price level P comes from a cost function“dual” to the production function, as discussed in later chapters).

But if saving is fixed, then there is no room in this system for an inde-pendently determined level of investment I. The principle of effective de-mand and a full employment Walrasian description of the economy areincompatible. In a Keynes-Kalecki world, the way to stimulate outputand economic growth is to raise investment; by reducing consumptiondemand, an increase in potential saving would have the opposite effect.If Walras rules, growth will be faster if there are increases in saving sup-ply (due to, for example, reductions in government spending). The twomodels give dramatically different policy recommendations, because ofthe causal relationships that they have built in. The question of howbest to “close” macro accounts such as those of Table 1.1 with an appro-priate set of behavioral hypotheses is one that arises throughout thisvolume.

Three further observations are worth making, before going on toother sets of accounts. The first is that in principle a construct like aSAM summarizes all that can be observed about economic transactionsat the macro level. It adds up all purchases and sales, incomes transferredand taxes paid, and so on in an economy at a “point in time” and aggre-

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gates them into certain categories. Economists, however, want to go be-yond mere observation and ask counterfactual questions about how Xmight change in response to a shift in I, how P might react to w, and soon (with the influences possibly running in the opposite directions aswell). We just went through two such exercises and will soon go throughanother.

Precisely because they are counterfactual, such thought experimentsare irrefutable. Cohorts of econometricians to the contrary, the best thatthe numbers extracted from a quarterly or annual sequence of SAMs cando is give correlations—how else could so many mutually contradictorymacro models have been “verified” on the basis of (say) American dataover time? As it turns out, both pairs (I, X) and (w, P) tend to move to-gether across SAMs. However, whether one variable causes the other inthe algebraic sense of the models worked out above is a query the datathemselves cannot answer. This is the major reason why macroeconom-ics is so theory driven, and why so many theories will have to be re-viewed in this book. To cull the good ones from the bad, to a large extentone has to go outside SAM-type data and bring in opinions about howindividuals and societies function as a whole, along with aesthetic crite-ria such as Occam’s razor (bearing in mind that parsimony is in the eyeof the beholder).

Second and related to the Occam question, the Keynes-Kalecki versionof macroeconomics has a clear, almost linear causal structure, as will beseen in Chapter 4. Imposing such an order on the macro system makesit possible to tell clean theoretical narratives. But it violates ingrainedWalrasian notions that the economy is a seamless web, everything de-pends on everything else in general equilibrium, and so on. In his Historyof Economic Analysis, Schumpeter (1954) reached back five genera-tions before Keynes to label his style of theorizing the “Ricardian vice.”The theories that David Ricardo and John Maynard Keynes constructedwere in their details quite dissimilar, but they both had crisp causal struc-tures. Whether vice or virtue was implicit is a question to be addressed insubsequent discussion.

Finally, in 1990s pop-culture imagery from the field of “chaoplexity”(a name blending chaos and complexity, coined by Horgan 1996), mac-roeconomics is an “emergent” phenomenon because its properties can-not be deduced solely from the individual economic actions of house-holds, enterprises, and players in financial markets. With regard to thefirst model above, for example, in The General Theory Keynes observesthat “the reconciliation of the identity between saving and investmentwith the apparent ‘free-will’ of the individual to save irrespective of whathe or others may be investing, essentially depends on saving being . . . atwo-sided affair. For . . . the reactions of the amount of his consumption

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on the incomes of others makes it impossible for all individuals simulta-neously to save any given sums. Every . . . attempt to save more by reduc-ing consumption will so affect incomes that the attempt necessarily de-feats itself” (p. 84). This typically macroeconomic scenario “emerges” inthe form of the quantity and price changes through which the “freewills” of individuals are forced to conform to the economy-wide ac-counting restrictions implicit in a SAM. This insight hovered at the edgeof economic theory for many decades after Adam Smith; only in the1930s did Keynes and Kalecki bring it into the full light of the principleof effective demand.

3. Disaggregating Effective Demand

As it turns out, the economy’s overall behavior is influenced not just bythe income distribution but also by differing forms of injections (invest-ment, government spending, exports) and leakages (saving, taxes, im-ports). In this section, we pursue that logic as applied to the U.S. macrosystem. Along the lines of Table 1.1, in macroeconomic equilibrium to-tals of injections and leakages must be equal. Broadly following Godley(1999), we can use this fact to set up a useful decomposition methodol-ogy for effective demand.

At the one-sector level (ignoring intermediate outputs and sales alongwith the distinction between wage and profit income flows), the aggre-gate supply of goods and services available for domestic use (X) can bedefined as the sum of total private income (YP), net taxes (T), and “im-ports” or (for present purposes) all outgoing payments on current ac-count (M):

X = YP + T + M. (1)

In NIPA categories, we have GDP = Yp + T = X − M so the accountingin (1) is nonstandard insofar as X exceeds GDP. As in row (A) of Table1.1, the aggregate supply and demand balance can be written as:

X = CP + IP + G + E, (2)

that is, the sum of private consumption, private investment, governmentspending (on both current and capital account), and “exports” or in-coming foreign payments on current account. It is convenient to defineleakage parameters relative to aggregate supply, yielding the private sav-ings rate as sP = (YP − CP)/X, the import propensity as m=M/X, and thetax rate as t = T/X.

From all this one gets a typical Keynesian income multiplier function

X = (IP + G + E)/(sP + t + m), (3)

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which can also be written as

X = (sP/λ)(IP/sP) + (t/λ)(G/t) + (m/λ)(E/m), (4)

in which λ = sP + t + m is the sum of the leakage parameters, and IP/sP,G/t, and E/m can be interpreted as the direct “own” multiplier effects onoutput of private investment, government spending, and export injec-tions with their overall impact scaled by the corresponding leakage rates(respectively, savings, tax, and import propensities). That is, aggregatesupply is equal to a weighted average of contributions to demand fromthe private sector, government, and the rest of the world. If two of thesecontributions were zero, then output would be equal to the third.

Another representation involves the levels of IP − sPX, G − tX, and E− mX, which from (4) must sum to zero. Moreover, the economy’s realfinancial balance can be written as

© + ‰ + ® = (IP − sPX) + (G − tX) + (E − mX) = 0, (5)

where © (= dD/dt), ‰, and ® stand respectively for the net change perunit time in financial claims against the private sector, in governmentdebt, and in foreign assets.

Equation (5) shows how claims against an institutional entity (the pri-vate sector, government, or rest of the world) must be growing when itsdemand contribution to X exceeds X itself. So when E<mX, net foreignassets of the home economy are declining, while G > tX means that itsgovernment is running up debt. A contractionary demand contributionfrom the rest of the world requires some other sector to be increasing lia-bilities or lowering assets, for example, the public sector when G > tX.Because from (5) it is true that © + ‰ + ® = 0, such offsetting effects areunavoidable.

The offsets, however, can cumulate over time. “Stock/flow” disequi-librium problems threaten when ratios such as D/X, Z/X, or −A/X (orD/YP, Z/tX, or −A/E) become “too large.” Then the component expres-sions in (4) and the accumulation flows in (5) have to shift to bringthe system back toward financial “stock-flow” or “stock-stock” equilib-rium. Such adjustments can be quite painful.

Without making predictions about whether the American economywill have recovered from its 2001–2003 slowdown (an outcome notknown as of this writing), it is interesting to see how its macro data fitinto equations (4) and (5) in the twentieth century. The lines in Figure1.1 show the evolution of supply and private, government, and foreigncontributions to effective demand since World War II, in nominal terms

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social accounts and social relations 15

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Figure 1.1Multiplier effects on output from each sector—trillions of nominal dollars (upper) and real dollarsof 1996 (lower).

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in the upper panel and in real terms below. Three observations can bemade.

First, since 1982, the “foreign” curve has generally been below thesupply line. This means that the external deficit (the excess of paymentsoutgoing on current account over those coming in) has had a contrac-tionary effect on economic activity, with current account leakages or im-ports outweighing injections or exports. This drag was briefly lifted inthe early 1990s, as a consequence of dollar devaluation of about 30 per-cent between 1985 and 1990 (which stimulated exports and cut back theimport share of supply), the (George H. W.) Bush recession (which alsoreduced import penetration), and transfers from the rest of the world ofabout $100 billion in connection with the Gulf War. All these favorablefactors receded after 1992, and the gap between supply and foreign ef-fective demand steadily widened, leading authors such as Godley (1999)and Blecker (1999a) to warn of impending stock/flow imbalances.

Second, governments at all levels—federal, state, and local—com-bined to stimulate demand through 1997. The federal deficit was re-sponsible for this outcome, because state and local governments sufferfrom chronic budget balances or surpluses. As the “government” curveshows, the policy choice to run a federal surplus to “pay down the debt”along with the fact that fiscal stimulus tends to drop off as the econ-omy expands (tax revenues rise and transfer payments such as unem-ployment compensation fall) led to a contractionary fiscal stance from1995 through 2000. Thereafter, government began to support demandagain.

Third, with demand from the rest of the world lagging and fiscal de-mand in retrenchment, in the late 1990s the private sector had to pick upthe slack. Its effective demand grew rapidly after 1992, because of risinginvestment and a falling saving rate. Private demand peaked at the end of1999, and with the onset of recession there was a very rapid decline. Bythe end of 2001 the private and public sectors were both offsetting thenet export drag, but with strongly divergent trends. It will be interestingto see if the two sectors go back to (respectively) dampening and sup-porting aggregate demand as they did from the mid-1970s through themid-1990s.

These demand shifts had financial consequences. As shown in (5), if asector’s effective demand lies above total supply, it has to borrow tofinance the excess. Quarterly increases in net claims among the sectorsare shown in Figure 1.2 (again, nominal data in the upper diagram andreal below). Two private sector curves are included, for household and“other” flows of investment minus saving (with the latter basically com-ing from nonfinancial and financial business).6 Except for the 1992 blip,

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social accounts and social relations 17

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U.S. imports consistently exceeded exports, E − mX < 0, so the econ-omy was decumulating net foreign assets.

Flow accumulation of government debt (G − tX > 0) reached its peakin mid-1992 and then declined; government began to build up positivenet claims—or reduce its net liabilities—in 1997. There was another re-versal in 1999–2000 and by 2001 the government sector once again wasrunning up debt in the range of $100–$200 billion per year. With an ex-ternal deficit on the order of $400 billion in nominal terms, the privatesector had to run the offsetting internal deficits.

Both components of the private sector behaved in unhistorical fashionin the 1990s. Ever since the early 1950s, the household sector had run aconsistently positive financial balance (or negative deficit in the figure)which beginning early in the 1970s tended to vary countercyclically be-tween around $300 billion in real terms in recessions and $100 billion inbooms. But beginning in 1992, the sector’s level of gross saving fell fromabout $600 billion to $200 billion in 2000. Investment rose from a bitover $200 billion to $400 billion. The outcome was that householdsstarted to run a historically unprecedented deficit in 1997.

The business sector had tended to run deficits during upswings andthen revert to approximate financial balance or a small surplus in reces-sions as in the early 1980s and early 1990s. But as with households, thebusiness deficit took off later in the 1990s. In 1991–92, both savingand investment were about $700 billion. They climbed in tandem (withinvestment rising somewhat faster) to about $1.0 trillion in 1997–98.Thereafter, investment shot up to almost $1.3 trillion in 2000, with sav-ing falling off to $850 million (with investment dropping significantlyfaster) in 2001. As Figure 1.2 shows, the swing of business into a consis-tent deficit position occurred in 1994–95; the household shift came ayear or two later. Thereafter both sectors’ deficits climbed hand in hand,amply collateralized by rising asset prices, into the bubble that began todeflate in the year 2000.

In other words, the Clinton boom was uniquely supported by net in-creases in private sector liabilities. The fiscal deficit played a negligiblerole in stimulating demand, in sharp contrast to previous upswings. Inthe first half of the 1990s, the public sector did issue liabilities to financethe foreign deficit. But in the second half of the decade private debtorstook over that function.

As of early 2003, how the rapid reversal of trends in private and pub-lic sector deficits in 1999–2000 will play out remains to be seen. Whatcan safely be said is that if the structural foreign deficit remains in the$400–$500 billion range and the household and business sectors con-tinue to move toward the combined surplus they used to run in economic

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downswings, then there will have to be a large fiscal stimulus if effectivedemand is to be maintained. Otherwise the foreign deficit will have to besharply reduced by recession and/or devaluation as in the early 1990s.Toward their right-hand sides, Figures 1.1 and 1.2 illustrate interestingtimes.

4. A More Realistic SAM

The next step is to introduce a more realistic set of accounts, bringing inelements missing from Table 1.1 with which macroeconomists have todeal on an ongoing basis. Table 1.2 illustrates some of the complica-tions.7

An initial extension is a more ample collection of economic actors,with incomes flowing to wage earners, “rentiers” or households receiv-ing dividends and interest, business enterprises, the banking system, thegovernment, and the rest of the world in rows (B) through (G) respec-tively. These six groups undertake financial transactions summarized inthe flows of funds rows (H) through (M). Underlying the accounts forsources and uses of incomes are the decompositions of production costsand demands for output in column (1) and row (A) respectively. Thesetake the same general forms as their analogs in Table 1.1, with new wrin-kles in column (1) related to taxes and foreign trade that are discussedpresently.

Turning to the details of sources and uses of incomes in rows (B)–(G)and columns (2)–(7), first note that in addition to their labor earningswbX (cell B1), wage recipients get (modest?) interest payments at rate ion the money (currency and deposits) Mw they hold as a claim on thebanking system (cell B5). More significantly, as discussed later, they re-ceive transfer payments Qw from the government in cell B6. In column(2), they use their income Yw for consumption PCw, taxes Tw, and savingSw. Rentiers make similar uses of their income Yr in column (3). Their in-come sources are interest earnings iMr in cell C5 and dividends on busi-ness equity that they hold in cell C4, where V is the amount of equityoutstanding, Pv is its price, and δ is the dividend payout rate.

In row (D), business income Yb is equal to gross profit flows πPX. Incolumn (4), part of Yb is used to pay interest on loans from abroad in cellG4 (i* is the foreign interest rate, e is the exchange rate in units of localcurrency to foreign currency, and Zb* is the stock of foreign loans to do-mestic business). Other uses include dividend payments in cell C4, taxesTb in cell F4, and local interest payments iLb in cell E4, where Lb is thestock of loans to business from the banking system and (for simplicity) itis assumed that the interest rate on both bank loans and deposits is the

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same.8 In cell J4, business saving Sb appears as retained earnings afterpayments for interest, dividends, and taxes. Banks’ income YI in row (E)comes from interest on loans to business and government (iLb and iLg incells E4 and E6 respectively) and interest on foreign reserves (i*eR* incell E7). In column (5), YI is used to pay interest on deposits and for sav-ing SI.9

In row (F), government income Yg comes from taxes on production (Tx

in cell F1), and income taxes on wage, rentier, and business incomes. Incolumn (6), Yg is used for public consumption PG as well as for trans-fers to wage earners (Qw) and interest payments at home (iLg) andabroad (i*eZ g*). Government wage payments that would appear in cellB6 are ignored, although as will be seen below they account for largeshares of GDP in most industrialized economies. The parenthesesaround government saving (Sg) suggest that its value is often less thanzero.10

Cell G1 shows one component of foreign income as imports scaled tothe gross value of output—a is the relevant input-output coefficient andthe “world price” P* of imports is implicitly set equal to one.11 Businessand government pay foreign interest in cells G4 and G6 respectively. Incolumn (7), foreign income is used to pay for “our” exports PE in cellA7, that is, national products are sold abroad at their local prices. As al-ready noted, in cell E7, the rest of the world pays interest at rate i* on thelocal currency value eR* of foreign reserves held by the banking system.

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Table 1.2 An expanded SAM with production, income, expenditure, and flow of funds accounts.

Current expenditures

Outputcosts Wages Rentiers Business Banks Government Foreign

Capitalformation

(1) (2) (3) (4) (5) (6) (7) (8)

(A) Output PCw PCr PG PE PIIncomes(B) Wages wbX iMw Qw

(C) Rentiers δPvV iMr

(D) Business πPX(E) Banks iLb iLg i*eR*(F) Government Tx Tw Tr Tb

(G) Foreign eaX i*eZ b* i*eZ g*Flows of funds(H) Wages Sw

(I) Rentiers Sr

(J) Business Sb −PI(K) Banks Sl

(L) Government (Sg)(M) Foreign Sf

(N) Totals PX Yw Yr Yb YI Yg Yf 0

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Consolidating row (G) and column (7) shows that “foreign saving” Sf isequal to the external current account deficit—if we are sending moremoney abroad than we are taking in, then the rest of the world is savingfor us.

The last use of output in row (A) is investment PI in column (8), whichincludes both gross fixed capital formation and the increase in businessinventories. Along row (A), consumption of households and govern-ment, exports, and investment sum to the gross value of output PX.Down column (1), PX emerges as the sum of wages (wbX), profits(πPX), and indirect taxes less subsidies on production activity (Tx) plusthe value of imports at domestic prices. The first three items make up to-tal value-added “at market prices,” or GDP (the sum of wbX and πPX iscalled value-added “at factor cost”).

From the equality of row (A) and column (1) totals, the national ac-counts breakdown of aggregate demand and the aggregate cost of pro-duction becomes P(Cw +Cr +G+ E+ I)− eaX=GDP=wbX+πPX+ Tx. As in last section’s discussion of effective demand, it is often conve-nient to work with X as an output indicator even though it is bigger thanGDP.

Next we turn to flows of funds. Wage earners in row (H) have the sim-plest financial account, with their saving Sw being directed solely towardan increment in money balances, w = dMw/dt in cell H11. To keep themathematics underlying Table 1.2 within the realm of simple calculus,

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Table 1.2 (continued)

Changes in national claims Changes in foreign claims

Businessequity

Bankassets Bank liab.

Nationalliab.

Nationalassets Totals

(9) (10) (11) (12) (13) (14)

PX

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− &Mw 0−PVv

.− &Mr 0

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− &L &M −eR&* 0&Lg eZ g

&* 0−eZ&* eR&* 0

0 0 0 0 0

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we assume that stock variables such as Mw increase or decrease smoothlyin continuous time. In row (I), rentiers use their saving to build upmoney holdings r in cell I11 and to acquire new equity PvÎ at the goingprice Pv in cell I9.

Business firms in row (J) have other financial options. The balancebetween business saving and investment varies widely across capitalisteconomies. In Japan, firms before the slump of the 1990s typically in-vested more than they saved, with household saving making up theshortfall. In abnormal circumstances such as those of Russia and SouthAfrica (for different reasons) in the 1990s, business saving substantiallyexceeded firms’ capital formation. As can be seen in Figures 1.1–1.2,prior to the go-go late 1990s, private saving in the United States (Sw + Sr

+ Sb) tended to exceed private investment (PI) by a margin in the rangeof $200 billion per year.12 Nevertheless, American business engages inmany financial transactions. In Table 1.2, for example, firms are as-sumed to have access to three sources of funds—new borrowing frombanks #b (J10), new borrowing from abroad e b

&Z* (J12), and new issuesof equity PvÎ (J9). In line with standard practice, incremental flows offoreign credits and equity are valued at their ruling prices, respectively eand Pv.

In row (K), sources of funds for banks are their saving SI in cell K5 andnew deposit liabilities in K11. Uses of these funds are for new loans #in K9 and acquisition of international reserves, e¦* in K13.13 In row (L),government’s (negative) saving Sg is covered by new loans from banks,#g, and from abroad, e g

&Z*.In Chapter 10, it will be shown that a row like (M) for the rest of the

world’s flows of funds with the home economy or the “balance of pay-ments” does not appear when a full SAM is set up for two countries. Thebalance of payments is no more than a derived set of flows that summa-rizes changes in the home country’s net foreign assets. However, in ac-counts for a single country it is convenient to carry a line saying that Sf orthe current account deficit must be offset by capital movements, that is,Sf + e¦* = e‰*.

Finally, note in columns (9) through (13) that changes in claims addup across different groups—in column (10) total new bank loans (#) goto business (#b) and government (#g), and so on. Summing the flows offunds rows (H) through (M) vertically gives the standard saving-invest-ment “identity,”

Sw + Sr + Sb +SI + Sg + Sf − PI = 0,

as a theorem following from Table 1.2’s other accounting balances. Asthe quotation from Keynes at the end of section 2 underlines, just howthis equation gets satisfied can be a complicated matter.

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5. Stock-Flow Relationships

The financial flows in Table 1.2 naturally cumulate over time. Also, theincrease in the capital stock K is the result of investment, = dK/dt = I(ignoring depreciation). The stock variables that are the outcomes ofthese processes appear in the balance sheets in Table 1.3. For each broadgroup of actors, assets are on the left and liabilities and net worth on theright.

As usual, wage earners have the simplest balance—their money hold-ings Mw make up their total net worth or wealth Ωr. Similarly, rentiers’money Mr plus the value of their equity holdings PvV add up to theirwealth Ωr. The government’s “asset” is the “full faith and credit” ∆ be-hind its debt obligations Lg and e gZ*—as will be seen in Chapter 6, somemodern macroeconomists do not take this sovereign claim very seri-ously. If we impose the accounting convention that the banking sec-tor does not save, it does not build up net worth. Foreign wealth Ωf ise(Z* − R*), or “our” external debt minus the banking system’s foreignreserves.

Analysis of the balance sheet for businesses is slightly more compli-cated. Their capital stock can alternatively be valued at “replacementcost” PK, or else at an “asset value” qPK. The “q” term was brought toprominence by James Tobin (1969), and represents the valuation put onfirms by financial markets.14 Under various interpretations, q will figurein much discussion to follow. At present, if business net worth Ωb in Ta-ble 1.3 is equal to zero, then “average” q is given by

q = (Lb + eZb* + PvV)/PK, (6)

or the ratio of enterprise total liabilities to the replacement cost of capitalstock. As will be seen in Chapter 4, one can restate this definition (at

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Table 1.3 Balance sheets corresponding to Table 1.2.

Wage Earners RentiersMw Ωw Mr Ωr

PvV

Business BanksqPK Lb

qPK eZ b*qPK PvVqP K Ωb

L MeR*

Government Rest of the World∆ Lg

∆ eZ b*eZ g* eR*eZ g* Ωf

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least formally) in terms of asset rates of return. Either way, q is often in-terpreted as a rough-and-ready indicator of the performance of firmsand figures as an argument in investment demand functions. A firm is ina sort of financial equilibrium when its q equals one. A higher value sug-gests that it should be building up its capital stock, and a lower one sig-nals that it may be ripe for an external takeover. The American mergerand acquisition wave of the 1980s (discussed in note 12 and later chap-ters) took place during a period when corporate q-values tended to bewell below unity.

A final point is worth noting before we take up how the flows of fundsin Table 1.2 and the balance sheets in Table 1.3 interact. Summing acrossall the balance sheets and equating demands and supplies for claims (forexample, Lb + Lg = L), gives the wealth “identity”

∆ + qPK = Ωw + Ωr +Ωb + Ωf.

In words, “primary wealth” is made up of the government’s debt (said tocome from “outside” the financial system) plus the capital stock valuedat its asset price. Through a web of financial claims, primary wealth con-stitutes the net worths of workers, rentiers, business, and the rest of theworld.

To begin to see the linkages of balance sheets with flows of funds, ob-serve that combining row (H) of Table 1.2 with the differentiated versionof the wage earners’ balance sheet gives the equalities

Sw = w = ôw.

That is, the change in workers’ net worth in the form of an increase inbank deposits is just equal to their saving.

For rentiers, similar maneuvers with their balance sheet and row (I) ofTable 1.2 give the result

Sr + ¯vV = Èr, (7)

or the capital gains on rentier’s holdings of business equity must beadded to their saving to arrive at their change in wealth. Note that levelsof wealth like Ωr only change over time and are constant in the “shortrun” unless an asset price like Pv discontinuously jumps. These account-ing restrictions help determine macro behavior, as will be illustrated inseveral later chapters.

The dynamics get more complicated for business net worth, for whichthe relationship is

Sb + (q − 1)¯I + ÉPK − ¯vV = Ωb. (8)

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To understand the implications of equation (8), one can work throughthree special cases.

First, suppose that q is identically equal to one (so that Ωb is identi-cally zero) and that ¯= Â= 0. Then (8) reduces to Sb = ¯vV, or enterprisesaving is automatically reflected into capital gains on equity. Under ap-propriate assumptions about capital accumulation and asset demands,this situation could correspond to the steady state of a neoclassical op-timal growth model (see Chapters 3 and 4 for examples). In such aworld, the financial structure of enterprises is a veil. They have no networth and their saving automatically redounds to the wealth of theirstockholders, that is, combining (7) and (8) gives Sr + Sb = ôr. Suchassumptions underlie the mainstream’s aversion to the class-differen-tiated saving behavior discussed above. If finance is a veil and identi-cal, “representative” households receive both wage and profit income,then diverse savings rates applied to different income streams make nosense.

Second, we can let q take values different from one but still set enter-prises’ net worth Ωb to zero. This is the financial world described bythe celebrated Modigliani-Miller (1958) theorem, discussed in detail inChapter 6. Still assuming ¯= Â= 0, business saving in (8) now shows upin changes in both q and Pv: Sb = ¯vV − ÉPK. The asset prices q and Pv

will also be linked by q’s defining equation (6). As shown in Chapter 4,plausible asset demand equations will determine both variables jointly.There is little substantive difference from the steady state case just dis-cussed. For the financial side of the economy the Modigliani-Miller theo-rem closely resembles a full employment assumption on the real side.These hypotheses lead naturally to models in which prices of goods andservices (on the real side) and rates of return to asset and liability claims(on the financial side) adjust smoothly to remove any incipient mar-ket disequilibria. Beginning with Keynes, structuralist economists haveviewed such models critically; they want to see a world in which real andfinancial quantity adjustments play essential roles.

Third, financial side structuralism comes into its own when businessnet worth Ωb is allowed to be nonzero, that is, asset markets do not in-stantaneously transform a firm’s valuation qPK into equity prices (giventhe levels of its other liabilities). Nonzero, endogenous net worth createsroom for independent dynamics (including possible jumps) for q and/orPv due to Keynes’s “animal spirits” or the forces producing “financialfragility” à la Hyman Minsky (1986). This world has a richer tapestryand is far less predictable than the two just discussed. It figures in someof The General Theory’s more dazzling insights but is alien to main-stream macroeconomics.

social accounts and social relations 25

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6. A SAM and Asset Accounts for the United States

To get a feel for the wealth of information that a social accounting ma-trix can convey, it makes sense to work through a numerical example.In this section we present a SAM—or rather a SAM plus supportingtables describing changes in asset/liability portfolios and the capitalstock—for the United States. The setup is somewhat different from thatin Tables 1.2 and 1.3 (and the SAMs in the rest of this book), which arebasically designed to summarize macroeconomic models set up in con-tinuous time. Rather, the emphasis in Tables 1.4–1.6 is on presenting theannual numbers as they appear in current prices in the U.S. NIPA andFOF accounts for 1999 (the latest year with a full set of data available asof this writing).

Rows and columns are given mnemonic labels based on terminologythat national income accountants like to use, for example, I-O for “in-put-output” at the northwest corner of Table 1.4 or A for “Absorp-tion of domestic final output” for the row immediately below. The ma-trix is organized with “headlines” for groups of rows—each number in aheadline row is the sum of the entries immediately below. Thus 6,286.8(billion dollars) in row H and column X is the sum of the “Householdand institution” income entries down through row HINT. Five sectorsare considered: households and institutions (including nonprofit entitiessuch as foundations and churches), nonfinancial business, financial busi-ness, general government (combining federal, state, and local),15 and therest of the world.16

The general layout of Table 1.4 resembles that of Table 1.2, but withdifferences in the details. One showing up immediately in columns XHthrough XG is that all four domestic sectors engage in “production.”The rationale is that sectors defined on an institutional basis both gener-ate income flows (thereby “producing” output in columns of the SAM)and receive those and other incomes in rows. This worldview contrastssharply with that of most formal macro models, which are set up interms of opposing categories like producers versus consumers, and soon. In NIPA-land, there is no conceptual overlap between, say, “house-holds” and “consumers.”

The entries in columns XH through XG are summed in column X. Asusual, the total of all entries or “gross value of output” in column X,10,543.4, corresponds to the sum of final demand items in row A. Grossdomestic product (GDP) can be defined as total absorption minus im-ports in cell (EIMP, X) or 10,543.4 − 1,244.2 = 9,299.2. A numericallyless significant fact is that financial business provides “business services”as an intermediate input into nonfinancial business. This flow is reflected

26 chapter one

Page 34: Reconstructing Macroeconomics: Structuralist Proposals and

in the positive and negative entries of 204.8 appearing in the I-O row(the number was extracted from the U.S. input-output table and nets re-corded payments flows going both ways).

Also in contrast to Table 1.2 (and the rest of the book), depreciationor “consumption of fixed capital” appears explicitly in Table 1.4. Forthe sectors, depreciation figures as a cost of production in rows HCFC,BCFC, and GCFC. Besides (mostly residential) depreciation of 163.2,the household production account (column XH) includes payments tolabor (row HW&S), rental income (HRIP) and a fairly hefty intrasec-toral interest flow of 340.4 (HINT) paid by households in their capacityas final owners and suppliers of factors of production to households intheir capacity as producers and users of those factors. There is also asmall net subsidy of −16.1 from government in row GTXI.17

Production accounts for nonfinancial business in column XN aremore complicated. Under the “Households and institutions” headlineare payments to labor in rows HW&S (wages and salaries) and HOLI(many “other” income flows). Incomes of proprietors of unincorporatedfirms appear in row HPI. The “Domestic business” headline covers pay-ment flows that stay within the corporate sectors themselves. For non-financial business the major items are undistributed profits (170.9 in rowBUDP), dividend and interest payments within the sector (250.9 and260.1 in rows BDIV and BINT), and depreciation of 715.7. Even omit-ting business direct taxes in cell (GTXD, XN), the nonfinancial busi-ness “surplus” of 1,415.6 amounts to 0.1797 of the sector’s output of7,876.4 (the column XN and row AN sum). In other words, the after-taxgross “profit share” of nonfinancial business is around 18 percent (or 22percent of nonfinancial business value-added = gross value of output −imports − intermediate inputs from financial business = 6,435.6).

Other headline payments include various forms of taxes of 1,118.7 togeneral government (row G) and imports of 1,236.0 from the rest of theworld (rows E and EIMP). As in Table 1.2, the accounting convention isthat imports of goods and services are undertaken by the business sec-tors for resale to the rest of the economy. Finally, in row Z there isa small discrepancy (−60.7) between the cost- and demand-side esti-mates of nonfinancial business activity. The accounting for financialbusiness in column XF is broadly similar. Its after-tax gross profit shareis 229.2/602.7 or a robust 38 percent. In relation to gross value added,the share is 229.2/799.3 = 28.7%.

Accounting for government in the SAM reflects the fact that separatecost- and demand-side estimates of its activities do not exist. “Produc-tion” of government services in column XG has two major components:depreciation of its capital in cell (GCFC, XG), and labor payments in cell

social accounts and social relations 27

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Table 1.4. Social accounting matrix for the U.S. economy: Generation, distribution,and uses of income, 1999 (billions of $).

Current account

Generation of income Uses of income

Total,resid.

sectors

House-holds &institu-tions

Non-financialbusiness

Financialbusiness

Generalgovern-ment

House-holds &institu-tions

Non-financialbusiness

X XH XN XF XG DH DN

CURRENT ACCOUNTNet purchases of

intermediateinputs

I-O 0.0 204.8 −204.8

Absorption ofdomesticfinal output

A 6,268.7

From households andinstitutions

AH 1,039.3

From nonfinancialbusiness

AN 4,669.4

From financialbusiness

AF 560.0

From generalgovernment

AG

Households andinstitutions

H 6,286.8 1,055.5 3,962.1 440.5 828.8 13.3

Wage and salarydisbursements

HW&S 4,475.3 408.5 3,068.4 346.2 652.2

Other labor income HOLI 501.0 297.1 27.3 176.6Proprietors’ income

with IVA and CCAdjHPI 663.4 596.5 66.9

Rental income ofpersons with CCAdj

HRIP 143.4 143.4

Consumption of fixedcapital

HCFC 163.2 163.2

Dividends HDIVInterest HINT 340.4 340.4Current transfers HTRC 13.3

Domestic business B(F&N)

1,644.8 1,415.6 229.2 535.2 881.5

Nonfinancial N 1,415.6 1,415.6Financial F 229.2 229.2 535.2 881.5Wage and salary

accruals lessdisbursements

BUDW 5.2 4.7 0.5

Undistributed profitswith IVA and CCAdj

BUDP 159.7 170.9 −11.2

Consumption of fixedcapital

BCFC 827.5 715.7 111.8

Dividends BDIV 328.9 250.9 78.0 314.9Interest BINT 283.8 260.1 23.7 535.2 566.6Current transfers BTRC 39.7 13.3 26.4

General government G 1,439.5 −16.1 1,118.7 140.8 196.2 1,490.5Indirect taxes less

subsidiesGTXI 689.7 −16.1 676.4 29.5

Contributions forsocial insurance

GTXW 323.6 275.7 22.0 25.9 338.5

Page 36: Reconstructing Macroeconomics: Structuralist Proposals and

Table 1.4 (continued)

Current account Capital account

Uses of income Investment

Financialbusiness

Generalgovern-ment

Rest ofthe

world

House-holds &institu-tions

Non-financialbusiness

Financialbusiness

Generalgovernment

Restof theworld

Netcapitaltrans-fers

NIPA &FOF

residuals Total

DF DG DE JH JN JF JG JE TRK ZNF T

0.0

1,325.7 990.2 408.1 1,158.4 138.2 254.1 10,543.4

1,039.3

305.9 952.5 408.1 1,158.4 138.2 243.9 7,876.4

5.0 37.7 602.7

1,014.8 10.2 1,025.0

1,350.5 986.5 −5.4 8,631.7

−5.4 4,469.9

501.0663.4

143.4

163.2

370.3 370.3963.8 1,304.216.4 986.5 1,016.2

370.5 357.0 280.3 4,069.2

370.5 1,786.1357.0 280.3 2,283.2

5.2

69.6 229.3

827.5

64.0 76.3 784.1306.5 357.0 134.4 2,183.4

39.7

93.1 3,023.1689.7

662.1

Page 37: Reconstructing Macroeconomics: Structuralist Proposals and

Current account

Generation of income Uses of income

Total,resid.

sectors

House-holds &institu-tions

Non-financialbusiness

Financialbusiness

Generalgovern-ment

House-holds &institu-tions

Non-financialbusiness

X XH XN XF XG DH DN

Direct taxes GTXD 255.9 166.6 89.3 1,152.0Consumption of fixed

capitalGCFC 170.3 170.3

Dividends GDIVInterest GINT

Rest of the world E 1,244.2 1,236.0 8.2 26.6Imports of goods and

servicesEIMP 1,244.2 1,236.0 8.2

Dividends EDIVInterest EINTCurrent transfers ETRC 26.6

CAPITAL ACCOUNTGross saving andcapital transfers

S 310.8 891.3

Households andinstitutions

SH 310.8

Nonfinancial business SN 891.3Financial business SFGeneral government SGRest of the world SE

Net purchases ofnonproduced assets

NPN

NIPA-FOFreconciliation

Q

Memo: Implied netlending NIPA

QLIN

Itemized discrepancyNIPA-FOF

QZIT

Memo: Conceptuallyadjusted netlending

QLCA

Residual discrepancyNIPA-FOF

QZZ

Net lending LHouseholds and

institutionsLH

Nonfinancial business LNFinancial business LFGeneral government LGRest of the world LE

Discrepancy Z −71.9 0.0 −60.7 −11.2 0.0 −0.1 0.0

Total T 10,543.4 1,039.3 7,876.4 602.7 1,025.0 8,631.7 1,786.1

Table 1.4 (continued)

Page 38: Reconstructing Macroeconomics: Structuralist Proposals and

Current account Capital account

Uses of income Investment

Financialbusiness

Generalgovern-ment

Rest ofthe

world

House-holds &institu-tions

Non-financialbusiness

Financialbusiness

Generalgovernment

Restof theworld

Netcapitaltrans-fers

NIPA &FOF

residuals Total

DF DG DE JH JN JF JG JE TRK ZNF T

1,407.9170.3

0.4 0.492.7 92.7

295.8 11.6 1,578.21,244.2

34.5 34.5251.4 251.4

9.9 11.6 48.1

173.2 342.2 313.2 0.0 2,030.7

−36.2 274.6

891.3173.2 173.2

342.2 36.8 379.0313.2 −0.6 312.6

7.2 −7.2 0.0 0.0

−2.9 −94.4 −26.1 0.0 −0.1 123.5 0.0

−133.5 −267.1 35.0 117.7 319.8 −71.9 0.0

−3.8 1.7 2.1 0.0 0.0

−129.7 −268.8 35.0 115.6 319.8 −71.9 0.0

0.9 −96.1 −26.1 −2.1 −0.1 123.5 0.0

−130.6 −172.7 61.1 117.7 319.9 −195.4 0.0−130.6 −130.6

−172.7 −172.761.1 61.1

117.7 117.7319.9 319.9

0.1 0.1 −0.1 0.0 0.0 0.0 0.0 0.0 0.0 71.9 0.0

2,283.2 3,023.1 1,578.2 274.6 891.3 173.2 379.0 312.6 0.0 0.0 0.0

Table 1.4 (continued)

Page 39: Reconstructing Macroeconomics: Structuralist Proposals and

(H, XG) plus social insurance contributions in cell (GTXW, XG). Howgovernment’s output of its own services filters over to the demand side ofthe economy is taken up below. For the moment, note that its labor-re-lated payments of 854.7 amount to almost 8 percent of the economy’soutput of 10,543.4.18

We next take up income generation and then go on to patterns of de-mand and savings. Besides incomes originating from production, house-holds and institutions receive relatively large inflows in the columnsheaded “Uses of income” (DH–DE). The biggest single item is 986.5 (9.3percent of total output) of transfers from general government in cell(HTRC, DG)—even in resolutely free enterprise America, the govern-ment plays a major redistributive role. Next in size are interest receiptsof 963.8 in cell (HINT, DF). This is intersectoral interest income. TheU.S. accounting convention is that all cross-sector interest and dividendpayments are channeled through financial business, that is, that sector issupposed to take in all such flows and then pass them along to their ulti-mate recipients (the United States lags countries such as Sweden in notproviding a full matrix of intersectoral movements of interest, dividends,and all other financial stocks and flows). Thus gross household interestreceipts in row HINT are the sum of intra- and intersector payments,340.4 + 963.8 = 1,304.2 (12.4 percent of total output and 15.1 percentof household income, largely to the benefit of institutions and persons inthe upper reaches of the size distribution of income).

Turning to the two business sectors, we find several interest paymentsflows in row BINT. Under the accounting convention just described,households pay 535.2 to financial business in cell (BINT, DH). To savewhite space in the SAM, only intersectoral interest payments figure incolumns DN and DF—nonfinancial business pays 566.6 to financialbusiness on its outstanding obligations, and 306.5 flows the other way.Similar observations apply to dividends in row BDIV. Finally there arenet undistributed profit, dividend, and interest payments from the rest ofthe world in column DE. As usual, they are assumed to go to financialbusiness for a total of 280.3 in cell (F, DE).

“General government” income largely comes from indirect taxes lesssubsidies (including a small subsidy to households, the total is 689.7,with the taxes paid by business), contributions to social insurance(662.1, from business, households, and the government itself), and di-rect taxes (1,407.9, with 82 percent coming from households). It also re-ceives minor dividend and interest payments from financial business.

Finally, the rest of the world’s income is from U.S. imports of goodsand services, dividends and interest channeled through financial busi-ness, and transfers. The total of 1,578.2 is 15 percent of the gross valueof output.

32 chapter one

Page 40: Reconstructing Macroeconomics: Structuralist Proposals and

The columns headed “Uses of income” are broadly similar to thosein Table 1.2, though affected by the maneuvers already discussed. Incell (AH, DH) households purchase 1039.3 “from themselves.” Thisamount is the household services “produced” with the cost structure ofcolumn XH. They also buy goods and services from the two businesssectors, pay intersectoral interest to financial business, render social in-surance payments and direct taxes to government, and make transfers tothe rest of the world. What’s left over is gross saving of 310.8 in cell (SH,DH). This flow amounts to 3.6 percent of household income. “Personalsaving” subtracts consumption of fixed capital (163.2 in row HCFC)from the gross figure, leaving 147.6 or 1.7 percent of income (subject toconsiderable media attention, this figure went negative for a time after1999). Aside from a small transfer to households in cell (HTRC, DN),19

nonfinancial business uses its income of 1,786.1 to pay interest and divi-dends to financial business in rows BDIV and BINT and to save 891.3 inrow SN. Financial business uses its income of 2,283.2 to distribute divi-dend, interest, and transfer payments to the other sectors and to save173.2 in row SF.

The government’s income is 3,023.1, or 29 percent of the gross valueof output. Its current demands for goods and services total 1,325.7 incell (A, DG). Adding government investment of 243.9 in cell (AN, JG),total purchases from business come to 554.8. The rest of the govern-ment’s spending takes the form of using its own-produced services of1,025.0 with the cost structure described in column XG emphasizing la-bor payments and depreciation (giving a total outlay of 1,579.8). In theUnited States at least, the traditional Keynesian injunction to “increaseG” 35 percent boils down to buying more goods and services from thebusiness sectors and the rest to hiring more government employees andcharging depreciation.

The rest of the world uses its income of 1,578.2 to purchase exportsfrom the United States and make payments (described above) to finan-cial business. Its “saving” or the U.S. current account deficit is 313.2 inrow SE. As noted above, this flow is interpreted as foreign saving be-cause the United States sends greater payments abroad than it takes in,covering the resulting deficit by emitting liabilities or running down ex-ternal assets. Both maneuvers feed into increased holdings of wealthabroad. In fact, the U.S. external deficit of a billion dollars per day ab-sorbs well over half of the rest of the world’s surplus of saving over in-vestment (Eatwell and Taylor 2000).

Sectoral investment demands—for gross fixed capital formation andchanges in inventories—are presented in columns JH through JE. Notethat household and nonfinancial business gross savings flows from rowsSH and SN fall sort of the corresponding investment levels by $100 bil-

social accounts and social relations 33

Page 41: Reconstructing Macroeconomics: Structuralist Proposals and

lion or so, and financial business and government savings exceed theirinvestments by lesser amounts. Some other sector must make up theoverall domestic savings shortfall—as noted just above and illustrated inFigures 1.1 and 1.2, this task gets passed to the rest of the world.

Table 1.4 does not follow Table 1.2 in using “flows of funds” rows tosummarize the changes in asset and liability holdings of the different sec-tors that are the financial counterparts of their differences between sav-ing and investment. This sort of information is presented in greater detailin Tables 1.5 and 1.6 below. To set up links with these stock-flow tables,we need to present net financial accumulation flows (or net increases infinancial claims) for each of the sectors. The numbers appear in Table1.4 under the headline “NIPA-FOF reconciliation.”

The word “reconciliation” suggests that the NIPA and FOF numbersare not consistent, which in fact is the case. But before we get into that,we have to complete the NIPA accounts. Their full definition (rathermore complicated than the simple saving-investment comparisons un-derlying Figure 1.2) of a sector’s financial accumulation or net lending toother domestic sectors and the rest of the world is

Net lending = (Gross saving + Net capital transfers receivable)− (Gross investment + Net purchases of non-produced assets).

Net capital transfers in column TRK are basically estate taxes; netpurchases of nonproduced assets in row NPN refer to mineral deposits,uncultivated forests, and so on (the two entries for transactions betweengovernment and the rest of the world are the only ones present in the ac-counts). The NIPA numbers that come out of the net lending balance ap-pear in row QLIN. The next row presents “itemized discrepancies” be-tween the two sets of accounts, with results in row QLCA.

The bottom lines are the FOF net lending estimates in rows LHthrough LE (summarized in row L) and the sectoral “residual discrepan-cies” between the two sets of estimates in row QZZ. The net lending es-timates feed into Table 1.5, subject to the caveat that some numbers inthe QZZ row are pretty big, for example, the nonfinancial business dis-crepancy amounts to almost $100 billion, or about 1 percent of the grossvalue of output and 10.7 percent of the sector’s gross saving. Such impre-cision is unavoidable in the economic statistical game.

The next step is to consider changes in holdings of financial assets,launched from rows LH through LE of Table 1.4 and presented in detailin the three sections of Table 1.5. As can be seen, financial instruments inthe table are classified under nine headings (consolidated from the thirtypresented at the highest level of aggregation in the “Flow of Funds Ma-

34 chapter one

Page 42: Reconstructing Macroeconomics: Structuralist Proposals and

social accounts and social relations 35

Tabl

e1.

5aN

etfin

anci

alas

sets

acco

unts

fort

heU

.S.e

cono

my,

1999

(bill

ions

of$)

.

Net

finan

cial

asse

ts(1

)M

oney

(2)

Oth

erba

nkcr

edit

(3)

Gov

ern-

men

tpa

per

(4)

Busi

ness

bond

s(5

)

Oth

erbu

s.pa

per

(6)

Mor

tgag

es(7

)

Hou

seho

ldin

vest

.&bo

rrow

ing

(8)

Equi

ty(9

)O

ther

(10)

FOF

sect

ordi

scre

p.(1

1)

Res

idua

lFO

Fdi

scre

p.(1

2)

Ope

ning

bala

nces

1748

.3−

508.

6−

207.

125

.40.

0−

31.9

0.0

0.0

0.0

2659

.9−

189.

312

6.4

Hou

seho

lds

and

inst

itutio

ns24

376.

841

39.5

51.0

1058

.658

4.7

0.0

−40

75.4

1198

6.1

1071

5.9

105.

7−

189.

312

6.4

Non

finan

cial

busi

ness

−17

706.

078

3.3

−10

72.6

−17

2.0

−18

29.6

282.

4−

1358

.216

5.9

−15

935.

914

30.6

0.0

0.0

Fina

ncia

lbus

ines

s−

1769

.5−

5393

.064

2.7

1962

.794

4.1

163.

552

63.3

−11

496.

854

09.7

734.

30.

00.

0G

ener

algo

vern

men

t−

4694

.717

0.9

158.

6−

4441

.761

.2−

525.

317

0.3

−65

5.2

102.

026

4.4

0.0

0.0

Res

toft

hew

orld

1541

.7−

209.

313

.116

17.7

239.

647

.50.

00.

0−

291.

812

4.8

0.0

0.0

Net

lend

ing

195.

4−

60.1

−32

.2−

3.1

−0.

1−

49.9

0.1

0.2

0.0

340.

30.

20.

0H

ouse

hold

san

din

stitu

tions

−13

0.6

208.

2−

20.5

154.

652

.6−

1.8

−43

1.8

300.

4−

387.

1−

5.1

−0.

1−

0.2

Non

finan

cial

busi

ness

−17

2.7

101.

4−

89.1

−17

.1−

229.

9−

41.8

−16

1.2

3.6

172.

788

.60.

10.

0Fi

nanc

ialb

usin

ess

61.1

−41

6.7

58.1

−28

1.9

18.2

58.2

588.

9−

265.

622

7.2

74.5

0.2

0.4

Gen

eral

gove

rnm

ent

117.

777

.65.

055

.512

.6−

22.9

4.2

−38

.23.

520

.30.

10.

0R

esto

fthe

wor

ld31

9.9

−30

.614

.385

.814

6.4

−41

.60.

00.

0−

16.3

162.

0−

0.1

−0.

2

Hol

ding

gain

s−

11.9

−2.

4−

29.9

−11

6.7

0.0

−60

.0−

0.1

−0.

20.

27.

618

9.5

−12

5.8

Hou

seho

lds

and

inst

itutio

ns42

53.2

−11

6.3

0.0

113.

073

.8−

60.4

−5.

412

01.7

2857

.30.

018

9.6

−12

6.0

Non

finan

cial

busi

ness

−37

48.0

0.0

0.1

0.0

0.0

0.0

−20

.624

.7−

3992

.124

0.0

0.0

0.0

Fina

ncia

lbus

ines

s13

.711

3.1

−29

.9−

171.

6−

31.7

−2.

6−

7.1

−12

26.6

1320

.949

.7−

0.5

−0.

4G

ener

algo

vern

men

t43

.1−

1.0

−0.

110

.00.

00.

433

.00.

09.

5−

8.5

0.0

0.0

Res

toft

hew

orld

−57

3.9

1.9

0.0

−68

.0−

42.1

2.6

0.0

0.0

−19

5.2

−27

3.5

0.5

0.6

Clos

ing

bala

nces

1931

.8−

571.

1−

269.

3−

94.4

−0.

1−

141.

90.

00.

00.

230

07.8

0.6

0.8

Hou

seho

lds

and

inst

itutio

ns28

499.

442

31.4

30.5

1326

.271

1.1

−62

.2−

4512

.613

488.

213

186.

010

0.6

0.2

0.2

Non

finan

cial

busi

ness

−21

626.

788

4.7

−11

61.6

−18

9.1

−20

59.5

240.

6−

1540

.019

4.2

−19

755.

317

59.2

0.1

0.0

Fina

ncia

lbus

ines

s−

1694

.7−

5696

.667

0.9

1509

.293

0.6

219.

158

45.1

−12

989.

069

57.8

858.

5−

0.3

0.0

Gen

eral

gove

rnm

ent

−45

33.9

247.

416

3.5

−43

76.2

73.8

−54

7.9

207.

5−

693.

411

5.0

276.

20.

20.

2R

esto

fthe

wor

ld12

87.7

−23

8.0

27.4

1635

.534

3.9

8.5

0.0

0.0

−50

3.3

13.3

0.4

0.4

Page 43: Reconstructing Macroeconomics: Structuralist Proposals and

36 chapter one

Tabl

e1.

5bG

ross

finan

cial

asse

tsac

coun

tsfo

rthe

U.S

.eco

nom

y,19

99(b

illio

nsof

$).

All

finan

cial

asse

ts(1

)M

oney

(2)

Oth

erba

nkcr

edit

(3)

Gov

ern-

men

tpa

per

(4)

Busi

ness

bond

s(5

)

Oth

erbu

s.pa

per

(6)

Mor

tgag

es(7

)

Hou

seho

ldin

vest

.&

borr

owin

g(8

)Eq

uity

(9)

Oth

er(1

0)

FOF

sect

ordi

scre

p.(1

1)

Res

idua

lFO

Fdi

scre

p.(1

2)

Ope

ning

bala

nces

7689

0.6

6508

.225

93.8

8558

.041

02.4

2985

.757

36.6

1575

9.1

1980

0.5

1078

3.0

−63

.212

6.4

Hou

seho

lds

and

inst

itutio

ns30

592.

641

39.5

276.

710

58.6

584.

710

9.3

1331

7.8

1071

5.9

326.

9−

63.2

126.

4N

onfin

anci

albu

sine

ss72

50.7

783.

33.

379

.416

05.6

122.

216

5.9

4491

.00.

0Fi

nanc

ialb

usin

ess

3181

1.5

896.

420

83.3

5302

.127

96.9

1089

.253

34.9

2254

.178

67.3

4187

.40.

0G

ener

algo

vern

men

t16

17.5

198.

315

8.6

500.

361

.212

4.3

170.

321

.310

2.0

281.

20.

0R

esto

fthe

wor

ld56

18.4

490.

772

.016

17.7

659.

616

6.6

1115

.414

96.4

0.0

Net

acqu

isiti

onof

finan

cial

asse

ts46

65.3

606.

830

2.1

601.

346

5.8

362.

261

3.6

556.

2−

53.9

1211

.20.

00.

0

Hou

seho

lds

and

inst

itutio

ns49

1.7

208.

242

.016

5.0

52.6

5.3

−0.

639

4.8

−38

7.1

11.6

0.1

−0.

2N

onfin

anci

albu

sine

ss72

5.8

101.

40.

9−

3.2

125.

216

.03.

648

1.9

0.0

Fina

ncia

lbus

ines

s25

69.0

175.

423

9.4

316.

724

0.0

246.

259

4.0

153.

523

1.6

372.

0−

0.2

0.4

Gen

eral

gove

rnm

ent

164.

874

.65.

037

.012

.66.

54.

24.

33.

517

.10.

0R

esto

fthe

wor

ld71

4.0

47.2

14.8

85.8

160.

6−

21.0

98.1

328.

60.

1−

0.2

Hol

ding

gain

s61

61.3

−11

.5−

30.2

10.4

42.5

65.3

25.9

1564

.044

73.2

84.7

62.9

−12

5.8

Hou

seho

lds

and

inst

itutio

ns42

58.9

−11

6.3

−0.

123

9.9

73.8

65.2

−0.

112

01.8

2857

.30.

463

.0−

126.

0N

onfin

anci

albu

sine

ss65

.624

.740

.90.

0Fi

nanc

ialb

usin

ess

1779

.310

5.7

−30

.1−

171.

6−

31.7

−2.

6−

7.1

337.

512

96.6

282.

70.

2−

0.4

Gen

eral

gove

rnm

ent

45.6

−1.

0−

0.1

10.0

33.0

9.5

−5.

80.

0R

esto

fthe

wor

ld11

.90.

1−

68.0

0.4

2.7

309.

8−

233.

4−

0.3

0.6

Clos

ing

bala

nces

8771

7.2

7103

.528

65.7

9169

.746

10.7

3413

.163

76.1

1787

9.3

2421

9.8

1207

8.9

−0.

40.

8H

ouse

hold

san

din

stitu

tions

3534

3.1

4231

.431

8.6

1463

.571

1.1

70.5

108.

614

914.

413

186.

033

8.9

−0.

10.

2N

onfin

anci

albu

sine

ss80

42.1

884.

74.

276

.217

30.8

138.

219

4.2

5013

.80.

00.

0Fi

nanc

ialb

usin

ess

3615

9.8

1177

.522

92.6

5447

.230

05.2

1332

.859

21.8

2745

.193

95.5

4842

.10.

00.

0G

ener

algo

vern

men

t18

27.9

271.

916

3.5

547.

373

.813

0.7

207.

525

.611

5.0

292.

5−

0.1

0.2

Res

toft

hew

orld

6344

.353

886

.816

35.5

820.

614

8.3

00

1523

.315

91.6

−0.

20.

4

Page 44: Reconstructing Macroeconomics: Structuralist Proposals and

social accounts and social relations 37Ta

ble

1.5c

Gro

ssfii

nanc

iall

iabi

litie

sac

coun

tsfo

rthe

U.S

.eco

nom

y,19

99(b

illio

nsof

$).

All

finan

cial

liabi

litie

s(1

)M

oney

(2)

Oth

erba

nkcr

edit

(3)

Gov

ern-

men

tpa

per

(4)

Busi

ness

bond

s(5

)

Oth

erbu

s.pa

per

(6)

Mor

tgag

es(7

)

Hou

seho

ldin

vest

.&

borr

owin

g(8

)Eq

uity

(9)

Oth

er(1

0)

FOF

sect

ordi

scre

p.(1

1)

Ope

ning

bala

nces

7514

2.4

7016

.828

00.9

8532

.741

02.4

3017

.657

36.7

1575

9.1

1980

0.6

8123

.125

2.6

Hou

seho

lds

and

inst

itutio

ns62

15.8

225.

741

84.6

1331

.722

1.2

252.

5N

onfin

anci

albu

sine

ss24

956.

70.

010

75.9

251.

418

29.6

1323

.214

80.4

1593

5.9

3060

.40.

0Fi

nanc

ialb

usin

ess

3358

1.0

6289

.414

40.6

3339

.318

52.8

925.

771

.613

750.

924

57.6

3453

.10.

0G

ener

algo

vern

men

t63

12.3

27.5

4941

.964

9.6

676.

516

.80.

0R

esto

fthe

wor

ld40

76.7

700.

058

.942

0.0

119.

114

07.1

1371

.60.

0

Net

incu

rren

ceof

finan

cial

liabi

litie

s44

69.7

666.

933

4.3

604.

446

5.9

412.

161

3.5

556.

0−

53.9

870.

9−

0.4

Hou

seho

lds

and

inst

itutio

ns62

2.2

62.5

10.4

7.1

431.

294

.416

.7−

0.1

Non

finan

cial

busi

ness

898.

590

.013

.922

9.9

167.

017

7.2

−17

2.7

393.

3−

0.1

Fina

ncia

lbus

ines

s25

07.8

592.

118

1.3

598.

622

1.8

188.

05.

141

9.1

4.4

297.

5−

0.1

Gen

eral

gove

rnm

ent

47.1

−3.

0−

18.5

29.4

0.0

42.5

−3.

2−

0.1

Res

toft

hew

orld

394.

177

.80.

514

.220

.611

4.4

166.

60.

0

Hol

ding

loss

es61

73.4

−9.

2−

0.3

127.

042

.512

5.3

26.0

1564

.244

73.0

77.1

−25

2.2

Hou

seho

lds

and

inst

itutio

ns5.

7−

0.1

126.

912

5.6

5.4

0.1

0.4

−25

2.5

Non

finan

cial

busi

ness

3813

.6−

0.1

20.6

3992

.1−

199.

10.

0Fi

nanc

ialb

usin

ess

1765

.8−

7.4

−0.

10.

115

64.1

−24

.323

3.0

0.4

Gen

eral

gove

rnm

ent

2.5

0.1

−0.

42.

70.

1R

esto

fthe

wor

ld58

5.8

−1.

842

.50.

150

5.1

40.1

−0.

2

Clos

ing

bala

nces

8578

5.4

7674

.631

35.0

9264

.146

10.8

3555

.063

76.1

1787

9.3

2421

9.6

9071

.1−

0.2

Hou

seho

lds

and

inst

itutio

ns68

43.7

288.

113

7.3

132.

746

21.2

1426

.223

8.3

−0.

1N

onfin

anci

albu

sine

ss29

668.

811

65.8

265.

320

59.5

1490

.216

78.2

1975

5.3

3254

.6−

0.1

Fina

ncia

lbus

ines

s37

854.

568

74.1

1621

.739

38.0

2074

.611

13.7

76.7

1573

4.1

2437

.739

83.6

0.3

Gen

eral

gove

rnm

ent

6361

.824

.549

23.5

678.

671

9.0

16.3

−0.

1R

esto

fthe

wor

ld50

56.6

776

59.4

476.

713

9.8

2026

.615

78.3

−0.

2

Page 45: Reconstructing Macroeconomics: Structuralist Proposals and

trix” tables of the FOF accounts): money, other bank credit, governmentpaper including “agency securities,”20 business bonds, other business pa-per, mortgages, household investment and borrowing, equity, and other.There are also columns for discrepancies.

Several accounting conventions differ between Tables 1.2 and 1.5. Inthe “Flows of funds” rows of Table 1.2, increases in liabilities are given apositive sign while increases in assets are negative. Tables 1.5a–c treattheir flow entries as being (normally) positive.

Second, Table 1.2 does not incorporate capital (or “holding”) gainsand losses on claims. They are carried in Tables 1.5a–c, subject to thebalance conditions:21

Opening balances of financial liabilities + Net increases infinancial liabilities + Holding losses on financial liabilities =Closing balances of financial liabilities

and

Opening balances of financial assets + Net increases in financialassets + Holding gains on financial assets = Closing balances offinancial assets.

Table 1.5a presents net financial accounts, consolidating asset and lia-bility positions. The first panel shows levels of stocks coming into 1999.The second panel gives financial accumulation flows by sector, with thenumbers coming from the “Net lending” panel of Table 1.4. The thirdpanel summarizes holding gains during 1999, and the fourth gives cur-rent value net asset positions at yearend.

In the first panel, households and institutions can be seen to have rela-tively large net holdings of money (4,139.5), government paper(1,058.6), equity (10,715.9), and “household investment and borrow-ing” or HIB (11,986.1). This last item combines a number of householdasset and liability categories, with details presented later. Other lines ofthe “Opening balances” panel show that equity is the biggest “liability”of nonfinancial business, while HIB is largely a net liability of finan-cial business. Households’ biggest net liability is mortgages (−4,075.4).Their net worth in early 1999 was 24,376.8, or 2.3 times that year’sgross value of output.

Nonfinancial business has net worth of −17,706.0. The chief net lia-bility item is equity (−15,935.9, reflecting the cumulative effect of the1990s bull market in stocks), followed distantly by business bondsand bank credit. Its net position with banks is only slightly negative(−289.3) because of its holdings of money. As might be expected, finan-

38 chapter one

Page 46: Reconstructing Macroeconomics: Structuralist Proposals and

cial business has a fairly complicated net portfolio position. Its liabilitycategories are money and HIB. It has large net asset holdings of govern-ment paper, business bonds, mortgages, and equity.

General government has negative financial net worth, with the big netliability being its bonds. The major net asset of the rest of the world isgovernment paper, including treasury and municipal bonds and agencysecurities.

The second panel shows net lending by the different sectors, comingfrom Table 1.4. Without going through all the numbers, the table’s strik-ing feature is that portfolio reallocations on the flow basis are as large asor larger than portfolio expansion due to net lending. Households, forexample, increased their holdings of money, government paper, and HIBby amounts substantially exceeding the absolute value of their net lend-ing flow of −130.6. They also increased their mortgage debt and randown holdings of equity. Both business sectors likewise practiced portfo-lio churning. The government mostly used its net saving of 117.7 tobuild up deposits and holdings of its own securities. The rest of theworld directed 162.0 of its saving of 319.9 to “Other” securities. TheFOF guide needs 36 pages to describe its Other category completely. Oneimportant component is foreign direct investment or FDI,22 in which theU.S. net position coming into 1999 was 119.2. At the end of the year, itwas 34.6.

As befits a bull market, net holding gains and losses during 1999are imposing. Households gain 4,253.2 and nonfinancial business loses−3748.0, with the big component being equity. Households also pick up1201.7 in their investment and borrowing transactions with financialbusiness, itself another major beneficiary of rising share prices. The restof the world had net holding losses of −573.9, on equity and “other.”

Asset and liability positions are presented in Tables 1.5b and 1.5c re-spectively. We just point to a few of the highlights. In Table 1.5c, it canbe seen that households enter 1999 with a debt level of 6,215.8, made upof mortgages (4,184.6) and loans under the HIB heading (1,331.7), thatis, consumer credit mostly coming from financial business. From Table1.4, the interest payment flow is 340.4 in cell (HINT, XH) on mortgages,of which 324.3 truly comes from households and the rest from nonprofitinstitutions. The implied interest rate on the opening balance is 8.1 per-cent (or 7.4 percent on the closing balance and 7.7 percent on the geo-metric mean of the initial and final levels of debt). Interest on consumerdebt is the difference between 535.2 from cell (BINT, DH) and 340.4 onmortgages, or 194.8. The implied rate on the initial balance is 14.6 per-cent (13.7 percent on the closing balance and 14.1 percent on the geo-metric mean).

social accounts and social relations 39

Page 47: Reconstructing Macroeconomics: Structuralist Proposals and

40 chapter one

Tabl

e1.

6Pr

oduc

edas

sets

and

netw

orth

acco

unts

fort

heU

.S.e

cono

my,

1999

(bill

ions

of$)

.

Net

wor

th(1

)

Net

finan

cial

asse

ts(2

)

Allp

rodu

ced

asse

ts(3

)

Fixe

das

sets

Inve

ntor

ies

(8)

Rev

isio

ndi

scre

panc

ypr

od.a

sset

s(9

)

Pre-

revi

sion

prod

uced

asse

ts(1

0)

Stru

ctur

esEq

uipm

enta

ndso

ftwar

e

Res

iden

tial

(4)

Non

resi

dent

ial

(5)

Res

iden

tial

(6)

Non

resi

dent

ial

(7)

Ope

ning

bala

nces

2686

5.2

1748

.325

116.

993

37.5

9976

.967

.644

09.2

1325

.6H

ouse

hold

san

din

stitu

tions

3327

9.1

2437

6.8

8902

.380

44.4

734.

723

.799

.5N

onfin

anci

albu

sine

ss−

6307

.1−

1770

6.0

1139

8.9

1079

.957

24.7

43.9

3224

.913

25.6

Fina

ncia

lbus

ines

s−

889.

7−

1769

.587

9.7

429.

345

0.4

Gen

eral

gove

rnm

ent

−75

8.8

−46

94.7

3936

.021

3.3

3088

.363

4.4

Res

toft

hew

orld

1541

.715

41.7

Net

incr

ease

bytr

ansa

ctio

n95

3.6

195.

475

8.2

252.

720

5.2

3.0

238.

858

.6−

39.6

797.

8H

ouse

hold

san

din

stitu

tions

128.

4−

130.

625

9.0

231.

717

.50.

98.

814

.124

4.9

Non

finan

cial

busi

ness

187.

1−

172.

735

9.8

18.8

104.

72.

117

5.6

58.6

−82

.944

2.7

Fina

ncia

lbus

ines

s11

9.0

61.1

57.9

15.6

42.3

31.5

26.4

Gen

eral

gove

rnm

ent

199.

211

7.7

81.5

2.2

67.3

12.0

−2.

383

.8R

esto

fthe

wor

ld31

9.9

319.

9

Incr

ease

bytr

ansa

ctio

n65

74.9

4665

.319

09.6

400.

045

2.1

8.8

990.

158

.6−

49.2

1958

.8H

ouse

hold

san

din

stitu

tions

913.

849

1.7

422.

135

6.3

32.5

2.9

30.3

14.0

408.

1N

onfin

anci

albu

sine

ss17

88.7

725.

810

62.9

38.4

263.

75.

969

6.3

58.6

−95

.511

58.4

Fina

ncia

lbus

ines

s27

43.3

2569

.017

4.3

27.3

147.

036

.113

8.2

Gen

eral

gove

rnm

ent

415.

216

4.8

250.

45.

312

8.6

116.

6−

3.7

254.

1R

esto

fthe

wor

ld71

4.0

714.

0

Page 48: Reconstructing Macroeconomics: Structuralist Proposals and

social accounts and social relations 41

Less

:Dec

reas

eby

tran

sact

ion

5621

.144

69.7

1151

.414

7.3

247.

05.

875

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−9.

611

61.0

Hou

seho

lds

and

inst

itutio

ns78

5.3

622.

216

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124.

615

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021

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163.

2N

onfin

anci

albu

sine

ss16

01.5

898.

570

3.0

19.6

159.

03.

852

0.7

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.771

5.7

Fina

ncia

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ines

s26

24.2

2507

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6.4

11.8

104.

64.

611

1.8

Gen

eral

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rnm

ent

216.

047

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8.9

3.1

61.3

104.

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170.

3R

esto

fthe

wor

ld39

4.1

394.

1

Hol

ding

gain

s73

2.5

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346.

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On the asset side in Table 1.5b, the household portfolio is quite diver-sified with big holdings of money, government paper, equity, and HIB.The large items in the latter basket are shares in mutual funds (2,501.0),bank personal trusts (1,001.0), life insurance reserves (718.3), and pen-sion fund reserves (an impressive 9,097.6).

Nonfinancial business has 7,250.7 in financial assets, over half ofthem “Other.” The dominant liability is equity. Financial business hasclaims of 31,811.5 on all other sectors and itself, under virtually allheadings (including 997.3 of mutual fund shares in HIB). Its total liabili-ties or “supplies” of finance are even larger at 33,581.0, concentrated inmoney, government paper (agency securities again), bonds, equity, other,and especially HIB. General government holds some assets, and its liabil-ities are concentrated under the heading of government paper. The restof the world’s liabilities are equity and other; its assets are spread underseveral headings.

Substantial churning is revealed under the “Net acquisition of finan-cial assets” and “Net incurrence of financial liabilities” headlines in Ta-bles 1.5b and 1.5c respectively; holding gains and losses are also large.Presumably all this financial activity underpins accumulation of physicalcapital. A summary appears in Table 1.6.

The first three columns of the table present summary net worth ac-counts, breaking net asset holdings into “financial” and “produced”(with the categories excluding nonproduced nonfinancial assets and alsoconsumer durables). The opening total of produced assets is 25,116.9,giving a capital/output ratio (with respect to the gross value of output)of about 2.4 in 1999. All four domestic sectors hold produced assets,with around 45 percent of the total in nonfinancial business and 35 per-cent held by households. Columns (4) through (7) give a breakdown of“fixed” assets by four categories. Most household fixed assets take theform of residential structures. Nonfinancial business holds all four typesof fixed assets plus a stock of inventories of 1,325.6 or 12.6 percent ofthe gross value of output.

Changes in holdings of produced assets are shown in panels lower inthe table. Households, for example, acquire 356.3 of residential struc-tures and dispose of 124.6 for a net increase of 231.7. The observed287.9 in holding gains on their houses (most of which are not “realized”for taxation purposes via actual sales of residences) gives an overall in-crease of 519.6 in the value of the housing stock.23

Similar decompositions apply to the other categories of produced as-sets. Though they are sizable (in the hundreds of billions of dollars), theincrements and decrements are smaller for physical assets in Table 1.6than for many financial categories in Table 1.5. Which broad asset cate-

42 chapter one

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gory wags what dog is an enduring question in macroeconomics, to beaddressed throughout the remainder of this book.

7. Further Thoughts

All the accounting discussed in this chapter reflects broad themes ofthis volume—there are many ways in which macroeconomic models canbe “closed” mathematically, with different “closures” reflecting diverseperceptions of socioeconomic reality. Such diverse formulations impingeon all aspects of the macroeconomy. Consider the variables already in-troduced in Tables 1.1–1.3:

Nominal prices and values: w, P, e, i, Pv, qP, etc.Real prices and distributional variables: ω, e/P, j = i − ¾,24 π, q, etc.Quantity variables: X, L, K, Cw, Cr, G, E, etc.Income flows: Yw, Yb, Yr, etc.Real and nominal accumulation variables: I, Sw, Sr, etc.Financial stocks (and associated flows): L, M, Z*, V, etc.

We obviously have a great deal to explain. The next chapter begins thetask by describing theories proposed over many years about income dis-tribution and price determination.

social accounts and social relations 43

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chapter two

z

Prices and Distribution

Can macroeconomics truly be grounded on social relations amongbroad groups of economic actors? An affirmative answer would run di-rectly counter to the reductionist program of mainstream economicsover the past few decades. Orthodoxy seeks to derive aggregate behaviorfrom micro-level decisions based on postulates of “methodological indi-vidualism” and “rational action” (or MIRA for short). MIRA-basedanalysis has spread throughout the social sciences,1 but it finds its fullestrepresentation in the theories of demand and supply of scarce resourcesbuilt into Walrasian microeconomics.

In the Walrasian context, methodological individualism asserts that“agents” (households, firms, investors, and so on) act solely in their owninterests, without direct, personal interactions of any sort. Each agentworks only with its set of “endowments” and the market opportunitieswhich permit it to alter that set’s composition. It makes these choices“rationally,” in light of built-in preferences among or technologies fortransforming commodities which are assumed to be predetermined.These postulates find their fullest expression in neoclassical theories ofprice formation, the topic of much of this chapter.

In a way, the following discussion is a detour from our main con-cerns, but price theory is an unavoidable input into the efforts in laterchapters to set out macrofoundations for microeconomic behavior. Inparticular, we will argue that through distributional channels, move-ments in “macro” prices like the interest rate, the exchange rate, and thewage can have profound effects on the economic possibilities of individ-uals and enterprises. As a prelude, it makes sense to examine conven-tional views about how they react to changing prices in their local eco-nomic environments.

1. Classical Macroeconomics

But before we get into MIRA price formation as such, both respect forhistory and ease of exposition point toward beginning with a review of a

44

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more macro theory of prices, that of the “classical” economists whoflourished from the late eighteenth through the mid-nineteenth centuries.The names that figure in this and the next sections’ discussion are thoseof the French physiocrats (especially François Quesnay), Jean-BaptisteSay, Thomas Malthus, David Ricardo, and Ricardo’s divergent succes-sors Karl Marx and John Stuart Mill.2

Quesnay’s Tableau Economique has the distinction of being the firstSAM in history, with a clear recognition of mutual transaction flowsamong landlords, manufacturers, and farmers.3 It shows an economyfirmly based on agriculture, with farmers producing food for everybodyand raw materials for manufacture, and landlords appropriating “sur-plus” product in the form of land rents. Such a macro structure was pos-tulated by all the early classical economists, and formed an essential partof their analyses.

One conclusion that the classicists drew from observing their rela-tively poor, largely agricultural countries was that most of what gotproduced found some economic use—in western Europe famines still oc-curred in the years around 1800 and were attributed to an overall scar-city of food. The largely empirical observation that creation of one prod-uct opens a “vent” for sales of others in exchange was enunciated by Sayin 1803, and came to be known as “Say’s Law.”

There were also business cycles (including the big post–NapoleonicWar downswing in England beginning in 1815) which were said to cre-ate “general gluts” of commodities not consumed. In the first edition ofhis Principles (1820) Malthus advanced arguments which (generouslyinterpreted) asserted that insufficient consumption by landlords mighthold down effective demand, leading to a general glut in the long run.Most classicists followed Say in asserting that gluts were transitory atworst. This analytical stance has implications that are worth pointingout.

First, there is no explicit theory of supply underlying Say’s (own) Law.Flows of commodities are produced by habitual actions of farmers andmanufacturers, and most are habitually used either as intermediates orto satisfy final demands. If Malthus’s landlords, like the leading charac-ters in Tom Jones, do their duty as enthusiastic spenders, there will be noglut.4

Second, there is no assertion that labor will be fully employed as inmodern versions of Say’s Law. How could there be full employmentwhen the poorhouse reigned? As will be seen, the classicists thought thatthe real wage was determined by social processes, not labor marketclearing.

Third, the macro balance implicit in the Tableau Economique impliesthat saving equals investment. Indeed, with full utilization of all com-

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modities, the quantities not used as intermediates, exported, or con-sumed must be invested—there is no other vent. The institutional struc-ture is such that capital formation is largely undertaken by the sameactors who save via their “abstinence,” so that the coordination prob-lems emphasized in Chapter 1 do not arise. It was pointed out, notablyby Mill, that the rate of interest could vary in the market for “loanablefunds” to help equate investment demand with saving supply. This ex-tension is best seen as a friendly amendment to Say’s Law.

Against this macro background, then, how did the classicists deter-mine income distribution and prices?

2. Classical Theories of Price and Distribution

There are two interpretations (at least). One, put forth by Alfred Mar-shall and developed more recently by Hollander (1979), is that in theirbasic instincts the classicists were neoclassical. They never quite figuredout marginal utility and productivity theory but came close—Ricardo’streatment of land rent being the prime example. In this narrative, thetheory of production that the classicists could not fully elaborate wouldpresumably have been some sort of cross between Walras’s and Mar-shall’s.

The other interpretation considered here is associated with the Univer-sity of Cambridge, post-Marshall. The simplest statement is that theclassicists took the vector of commodity output flows as given by non-economic processes having to do with traditional agricultural practices,guild hall rules for craft production, and so on. However, they did setforth variants of a distribution-driven theory of price, later highly elabo-rated in Piero Sraffa’s (1960) book on Production of Commodities byMeans of Commodities and subsequent contributions. Essays in the col-lection edited by Eatwell and Milgate (1983) take the further step ofcombining Sraffian price theory with determination of output not bySay’s Law but by effective demand. Whether prices and quantities can beso neatly separated is a complication to be discussed presently.

Two versions of classical price theory are presented here. The first setsout “prices of production” in two incarnations involving circulating andfixed capital respectively. The second embeds prices of production withfixed capital into a “natural” accounting system proposed by Pasinetti(1981).

In modern notation, the basic accounting scheme with circulating“capital” takes the form of intermediate goods in process in N sectors.(The sectors are indicated in the usual fashion by i and j subscripts,which should be fairly easy to distinguish from the i and j labels used

46 chapter two

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throughout this book for nominal and real interest rates respectively.)Cost decompositions for the sectors take the form

PjXj = P Xi ij

i

N

=

∑1

+ Wj + Πj, j = 1, . . . , N (1)

where Pj and Xj are respectively the price and output of commodity j, Xij

is the intermediate use of commodity i in the production of commodity j,and Wj and Πj are respectively wage and “surplus” (rent, profit, etc.)flows in sector j.

Prices of production models add two hypotheses to this accounting.First, input-output coefficients of the form aij = Xij/Xj are stable in theface of “reasonable” variations in prices and quantities. Second, wageand profit rates per unit of labor and capital respectively are equalizedacross sectors.

The accounting in equation (1) and first hypothesis are not strikinglycounterfactual. The second hypothesis is, meaning that prices of produc-tion are often interpreted as “centers of gravitation” toward which pro-cesses of competition will make observed sectoral prices tend as capitaland labor are reallocated across sectors as their respective returns in allproductive activities tend toward equality. In a standard example, ifwages are paid at the end of the period of production and surpluses aregenerated by a real interest rate j charged on the use of circulating cap-ital, then “in the long run” in a two-sector model the price system will begiven by the equations

P1 = (1 + j)(P1a11 + P2a21) + wb1 (2)P2 = (1 + j)(P1a12 + P2a22) + wb2,

where w is the wage. Both j and w are assumed to apply economy-wide.Wage bills are Wj = wbj and surplus flows are Πj = j(P1a1j + P2a2j)Xj for j= 1, 2.

If one price (say, P1) is taken as a numeraire, then (2) will solve for therelative price P2/P1 and either the real wage w/P1 or the interest rate j. Inother words, if in the long run competition equalizes rates of paymentsacross sectors and social processes set one of the two distributional vari-ables w/P1 or j, then relative prices and the other distributional variablewill follow. In Garegnani’s (1984) description, the value and distribution“core” of the macroeconomic system is determined independently ofoutput levels, so long as the aij coefficients are stable.

The story is broadly similar in models with fixed capital. GeneralizingTable 1.1, an economy-wide two-sector SAM for this case appears in Ta-ble 2.1. For the moment, we concentrate on the cost decompositions in

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columns (1) and (2), which give price equations of the form Pi = wbi +πiPi, where w again is the economy-wide wage rate, bi is the sector i la-bor-output ratio and πi is its profit share.

Suppose that the first sector produces consumer goods and the secondcapital goods (leaving intermediates in accounting limbo, as is often thecase in macro models). Also, let each sector’s “technically determined”capital/output ratio be µi and r be the “pure” rate of profit on fixed cap-ital, equalized across sectors.5 The value rate of profit will be rP2, be-cause P2 is the market price of capital goods. If nonwage income is en-tirely made up of profits, by definition we have r = πiPiXi/P2Ki, where Ki

is sector i’s capital stock. Because µi = Ki/Xi, we get πiPi = rP2µi. Finally,letting ω = w/P1 be the real wage and ρ = P2/P1 be the relative price ofcapital goods, we can write the cost decompositions as

1 = ωb1 + rρµ1 (3)ρ = ωb2 + rρµ2.

This system has three unknowns—ω, r, ρ. Again, given one of the dis-tributional variables r and ω, we can solve for the other distributional in-dicator as well as relative prices. Classicists typically invoked costs of re-production of human labor or a reserve army of the unemployed to peg avariable like ω. In Chapter 7, we will see how such ideas along withGaregnani’s “core” carry through into recent structuralist models.

Distributional conflict can be underlined if we eliminate ρ from equa-tions (3) to get a relationship known as the “wage-profit curve” or “fac-tor-price frontier”:

(1/ωr)(1 − ωb1)(1 − rµ2) = b2µ1. (4)

48 chapter two

Table 2.1 A SAM for Pasinetti’s “Natural System.”

Sec. 1 Sec. 2 WagesProfits Capital formation

Totals(1) (2) (3) (4) (5) (6) (7) (8)

Output uses(A) Sec. 1 P1C P1X1

(B) Sec. 2 P2gµ1X1 P2gµ2X2 P2X2

Sources of incomes(C) Wages wb1X1 wb2X2 Yw

(D) Sec. 1 profits π1P1X1 Yπ1

(E) Sec. 2 profits π2P2X2 Yπ2

Flows of funds(F) Sec. 1 S1 −P2gµ1X1 0(G) Sec. 2 S2 −P2gµ2X2 0(H) Totals P1X1 P2X2 Yw Yπ1 Yπ2 0 0

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It is easy to see that the partial derivatives of the left-hand side with re-spect to both ω and r are negative. The implication is that there is an in-verse trade-off between the real wage and the profit rate, or if one broadclass of income recipients gains the other inescapably loses. This sort ofclass conflict characterizes many classical and neoclassical macro mod-els, and often hinges on Say’s Law. If output levels were to rise in re-sponse to distributional changes, for example, then both workers andprofit recipients could gain because of the resulting decreases in the µi ra-tios in (4).

Finally, note that if b1/µ1 = b2/µ2 then (4) simplifies to the linear formωb1 + rµ2 = 1. This famous case of “equal organic compositions of cap-ital” (or equal labor/capital ratios) across the two sectors is one in whichdistributional conflict is quite clear. If we scale coefficients so that b1 = b2

= b and µ1 = µ2 = µ, then P2 =ωb/(1− rµ)= P1 so that a labor theory ofvalue applies—prices in both sectors are formed with the same markuprate on labor costs. The markup factor (1 − rµ)−1 increases when theprofit rate r goes up.

In practice, profit rates across different sectors (and firms) neverequalize but on the other hand they rarely differ by more than a factor oftwo or so. In industrialized economies, wages make up the larger pro-portion of value-added and even variable costs. Hence a labor theory ofvalue is not a bad empirical approximation—Ricardo’s perception, asStigler (1958) famously pointed out. Marx, however, turned the labortheory into a political question by tying it to surplus extraction or ex-ploitation. Since then, generations of progressive economists have toiledto set out analytical conditions delineating circumstances in which priceswill be formed as simple markups on labor costs. Three cases in whichsuch a price theory is valid are of interest.

First, as just noted, there can be equal organic compositions of capitalacross sectors.

Second, Sraffa (1960) discovered in a circulating capital model that ifa special set of weights is used to construct an economy-wide price index(based on the ruling set of prices), then a linear wage-profit curve fallsout of the computation. The weights make up a “standard commodity”characterized in two sectors by equality of the ratios Xi/(ai1X1 + ai2X2), i= 1, 2. The proportions of total output to intermediate sales are thesame across sectors, and in fact equal 1 + j*, where j* is the highest realinterest rate the system will support when the wage w is set to zero in (2).In terms of the standard commodity, prices can all be reduced to theircontent of direct-and-indirect or “dated” labor. What Sraffa cleverly didwas to choose his index weights to mimic the effects of a “technologi-cally” determined equal organic composition.6

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He also Delphically suggested that the real interest rate on circulatingcapital “is susceptible of being determined from outside the system ofproduction, in particular by the level of the money rates of interest”(p. 33). How the structure of “own-rates of return” to physical andfinancial assets anchored by the short-term financial interest rate mightserve to set all asset prices and corresponding profit rates was a themedeveloped by Sraffa, Keynes, and Kaldor. It is discussed in Chapter 4.

A third example of a labor theory of value is Pasinetti’s “natural sys-tem” exemplified in Table 2.1. It configures saving and investment flows(instead of technical coefficients or a commodity bundle) to fix each sec-tor’s price as a markup on its output’s labor content.7 In the Table 2.1SAM, it can be seen that as in Table 1.1, all wage income is consumed(cell A3). Pasinetti accepts Say’s Law in its modern, full employment ver-sion, so that total employment b1X1 + b2X2 equals labor supply &. Com-bining this assumption with row (C) and column (3) gives C=ω&—con-sumption equals the real wage times the labor supply.

Investment demand in Table 2.1 is based on the premise of steady-state growth. Output and the capital stock in each sector grow at thesame rate g: i = µi†i = µigXi, where in the absence of technical progressg is also the growth rate of the labor force. Cells B6 and B7 show the re-sulting purchases of commodity 2. The last key assumption is that in-vestment in each sector is directly financed by its own profit flows—atthe industry level there is no discoordination between abstinence andcapital formation.

As noted in connection with Tables 1.2 and 1.4, this hypothesis is notstrictly valid, because enterprises typically pay over some share of theirprofit flows to households and financial intermediaries as dividends, in-terest payments, and so on, and also tap the financial system for funds topay for part of their investment demand. The relevant empirical questionis whether or not fully self-financed investment is a plausible first ap-proximation. As illustrated in Figure 1.2 and Table 1.4 for the UnitedStates, Pasinetti’s assumption may not be completely misleading (if weignore the bubble of the late 1990s). Retained earnings of the businesssector more or less track its gross capital formation, and household sav-ing somewhat exceeds investment in housing. The household net lendingposition is roughly equal to business borrowing.

If self-financing applies, equating profit and investment flows in eachsector shows that ri = πiPi/P2µi = g. Profit rates across sectors equalize tothe economy-wide rate of growth—a situation that modern neoclassicaleconomists call the “golden rule” after Phelps (1961).8 From columns (1)and (2) of Table 2.1 the price equations become Pi = P2gµi + wbi, withsolutions

50 chapter two

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P1 = [w/(1 − gµ2)][b1 + g(µ1b2 − µ2b1)] (5)P2 = wb2/(1 − gµ2).

In sector 2, a simple markup applies. In sector 1, the price depends on la-bor content wb1, but the relationship involves the expression (µ1b2 −µ2b1), which measures the difference in organic compositions betweenthe two sectors. As emphasized by Pasinetti, similar rules apply in themore complicated case in which growth (and profit) rates differ acrossindustries.

A labor theory of value (though with sector-specific price/wage rela-tionships except when there are equal organic compositions in both sec-tors) emerges from Pasinetti’s system, essentially from his assumptionsabout how investment is financed. A result about income distributionwhich will figure in later chapters also follows. Suppose that the capacitygrowth rate g increases, requiring additional investment. An output ad-justment of the Keynes-Kalecki sort cannot occur, because full employ-ment is presupposed in the natural system. The saving counterpart canonly come from increases in operating surpluses πiPi or (as can be veri-fied by manipulating equations (5)), a fall in the real wage ω and work-ers’ consumption ω&.

This sort of crowding-out of consumption by a greater injection ofinvestment demand is known as “forced saving,” whereby the extrasaving effort is extracted by income redistribution from (in the pres-ent case) low-saving workers to high-saving firms. After World War II,macroeconomic adjustment via forced saving was emphasized mainly byNicholas Kaldor (1957). Three decades previously it had figured as themain equilibrating mechanism in Keynes’s Treatise on Money (1930),Schumpeter’s Theory of Economic Development (1934), and the macro-economics of a whole generation that Amadeo (1989) calls the “post-Wicksellians.”

The bottom line to the foregoing discussion of classical price theory(and even the labor theory of value) is that it is not likely to be far wrongas a “center of gravitation” in a circulating capital model or even a fixedcapital model so long as output levels and thereby the capital-output ra-tios µi are fairly stable. But if Say’s Law for commodities does not gener-ally hold, then it is conceivable that effective demand at the sectoral levelwill be sensitive to income distribution. More precisely, demand-deter-mined output levels Xi may respond to changes in the real wage andprofit rates, which themselves depend on the Xi via the ratios µi = Ki/Xi.Classical supply-side determination of output ceases to apply. Such po-tential linkages between distribution and effective demand did not figurein classical theory (save perhaps for the work of the perpetually muddled

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Malthus), but are central to the structuralist models discussed in laterchapters. They are not considered in the classically influenced paperscollected in Eatwell and Milgate (1983), which, as already noted, sug-gest that a reasonable macro framework ought to combine Ricardianprice theories with determination of output by effective demand. Thisprogram has problems if demand depends strongly on income distribu-tion as captured in most macro models by the values of variables such asω and r. As will be seen, there are reasons to believe that such linkagesexist.

3. Neoclassical Cost-Based Prices

The emphasis switches wholly to the supply side in neoclassical pricetheory. The base case is pure competition in input markets, with theMIRA individuals being “small” firms hiring inputs according to theirmarket prices. The model’s emphasis is on adding substitution wrinklesto prices of production, turning a parameter like the labor-output ratio b= L/X into a function of the real wage as well as of other real inputprices. Such details appear clearly in a “dual” specification which usescost instead of production functions to describe price formation and in-put demands. In this section we spin the basic story, and then go on to acouple of applications.

To begin with the traditional production function, assume that a firmcan produce output X using inputs Z1 and Z2 according to a “technical”relationship such as X = F(Z1, Z2). The usual hypothesis added for mac-roeconomics is that the “aggregate” production function F(..) demon-strates constant returns to scale or CRS (in other words, F(..) is homoge-nous of degree one so that for a positive constant κ, we have F(κZ1, κZ2)= κF(Z1, Z2)). As is well known, if the firm pays its inputs their marginalproducts, then from Euler’s Theorem under CRS the total value of pay-ments will just exhaust the value of output. Moreover, average cost perunit output will be independent of the scale of production.

If the real market price of input i is ci, then the firm is supposed to min-imize the total cost Γ = c1Z1 + c2Z2 of producing a given level of outputX. Let the function C(c1, c2) be equal to the value of Γ when the firm haschosen its cost-minimizing input basket. “Duality” means that the fol-lowing production and cost relationships apply:

Production CostX = F(Z1, Z2) Γ = C(c1, c2)∂F/∂Zi = ci, i = 1, 2 ∂C/∂ci = Zi, i = 1, 2

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In the literature, the result that the partial derivative of the cost func-tion with respect to an input’s price gives the level of use of that input isknown as Shephard’s Lemma (1953). Setting the partial derivative of theproduction function with respect to an input (the “marginal product”)equal to its cost is the standard rule for determining input demand.

It is easy to sketch a proof of Shephard’s Lemma using the “envelopetheorem” about the behavior of functions which have been optimizedwith respect to some of their arguments. For example, let M(y) be thevalue that the function f(x, y) takes when it is minimized with respectto x,

M(y) = min f(x, y) = f [x(y), y], (6)x

where x(y) is the x that solves the minimization problem for a given y.The question is what happens to M(y) in (6) when y changes. The an-

swer is that dM/dy is equal to the partial derivative of f with respect to y,holding x to its optimized value. In Shephard’s Lemma, for example, thederivative of the cost function Γ = c1Z1 + c2Z2 with respect to c1 whenthe Zi are at their optimal values is just Z1. Because Z1 and Z2 have al-ready been chosen to minimize cost, any “small” or “second-order”changes (d2Z1/dc1

2 and d2Z2/dc12 ) they make in response to shifts in c1 will

not reduce Γ any further.9

A first example illustrates further implications of duality. Switching tomacroeconomic labels for inputs, suppose that X is produced by labor Land capital K. The output price level is P and the nominal wage is w. Inthe characteristic aggregate contortion mentioned in Chapter 1, capitalgoods are assumed to be made of the same “stuff” as X, meaning thattheir replacement cost is also P, as opposed to a specific capital cost in-dex PK (which, for example, in a small open economy depending on cap-ital goods imports would surely depend on the exchange rate e). With apure profit rate r, the nominal cost of using capital is rP.

A commonly used production function presupposes a constant elas-ticity of substitution (CES), with the elasticity σ being a measure of thecurvature of an isoquant.10 The explicit form of a CES production func-tion is

X = [βLL−λ + βKK−λ]−1/λ, (7)

where λ = (1 − σ)/σ and the βi are scaling parameters which can be esti-mated using the payment shares of inputs in the value of output. Setting

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the partial derivatives with respect to L and K equal to the real wage ω(= w/P) and profit rate r give input demand functions as

L = X(ω/βL)−σ and K = X(r/βK)−σ. (8)

Input demands are proportional to the output level X, with the new twistbeing that the input coefficients or factors of proportionality between in-puts and output (the terms in parentheses taken to the power −σ) nowdepend on real costs. The same is true of input shares ψ = wL/PX and1 − ψ = π = rK/X.

A CES cost function has the same functional form as the correspond-ing production function, a convenience demonstrated by plugging theexpressions in (8) into (7) and rearranging:

P = [γLw1−σ + γK(rP)1−σ]1/(1−σ) or 1 = (γLω1−σ + γKr1−σ)1/(1−σ), (9)

where γi = (βi)σ, for i = K, L.The second equation in (9) shows that the real wage ω and profit rate r

vary inversely—if one falls the other must rise as along the classicalwage-profit curve (4) discussed above. The first equation makes P into alinearly homogeneous function of nominal input costs w and rP, not dif-ferent in spirit from the prices of production relationships (1) and (2). Bypermitting its input coefficients and cost relationships to depend on rela-tive prices, neoclassical production theory generalizes classical theory toa degree, but the differences between the two approaches are not pro-found.

4. Hat Calculus, Measuring Productivity Growth, and FullEmployment Equilibrium

In practice, much of the neoclassical story follows from accounting iden-tities, as an extended example in this section illustrates. It relies on a use-ful bag of tricks known informally as “hat calculus,” where a “hat,” orcircumflex accent, over a variable denotes its logarithmic differential (orlog-change): “X-hat” = ¼ = d(log X) = dX/X.11 As already observedin Chapter 1 (note 24), one can also interpret ¼ as a growth rate, that is,¼ = †/X = (dX/dt)/X.

We can begin with a version of the “Output cost” columns of theSAMs already presented:

PX = wL + rPK,

where we ignore interindustry transactions, taxes and transfers, andother complications. This equation is a cost function like the expressions

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in (9), but with less regalia. Log-differentiated and rearranged, it can bewritten in the form

¾ + ¼ = ψ(œ + ü) + (1 − ψ)(¹ + ¾ + ú),

where as before ψ is the share of labor payments wL in the value of out-put PX. For this formula to be able to track changing SAMs, ψ wouldhave to shift over time (contrary to the Cobb-Douglas case, for exam-ple). The algebra can be rearranged to give a decomposition of quantityand price log-changes in “Divisia indexes” with time-varying weights ψand (1 − ψ):

0 = ψ[(œ − ¾) − (¼ − ü)] + (1 − ψ)[¹ −(¼ − ú)], (10)

where the hats implicitly signify growth rates.Several general points can be made regarding (10). The first is that the

terms (¼ − ü) and (¼ − ú) respectively measure shifts in the output/la-bor and output/capital ratios, or average “productivity” levels of thetwo inputs. Long-run evidence reviewed by Foley and Michl (1999) sug-gests that observed technical change (as reflected in shifting productiv-ity levels) in capitalist economies is sometimes but not always “Marx-biased” in the sense that labor productivity X/L tends to rise over timewhile capital productivity X/K falls.

Another “stylized fact” often but not always supported by the dataand built into many growth models is that real wage growth (œ − ¾)tends to run at about the same rate as labor productivity growth (¼ −ü), when both variables are averaged over time. If this relationship is ob-served, then persistently negative trend growth (¼ − ú) in capital pro-ductivity has to be associated with a falling rate of profit (¹ < 0) in (10),because the bracketed term multiplied by ψ will be close to zero. Marx-biased productivity changes go together with the traditional Marxist dis-tributive theme that a falling rate of profit (FROP) is to be expected un-der modern capitalism.

Of course, observed country histories add complications. The plots inFigure 2.1 present growth rates for the real wage and (nonresidential)capital and labor productivity levels in the United States (lower diagram)and Japan (upper) after the Japanese “miracle” period ended in the mid-1960s. The data are presented year-on-year, to give some feeling for cy-clical fluctuations.

Capital productivity in the United States has fluctuated strongly, basi-cally in step with the business cycle. The growth rate’s jumps up anddown, however, are close to being centered around zero (the averagegrowth rate is 0.0008). Early in the period, growth rates of labor pro-

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56 chapter two

Japan: growth rates in real compensation, capital and labor productivity

−0.15

−0.10

−0.05

0

0.05

0.10

0.15

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

U.S.: growth rates in real compensation, capital and labor productivity

−0.060

−0.050

−0.040

−0.030

−0.020

−0.010

0.000

0.010

0.020

0.030

0.040

0.050

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

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1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

Growth rate inlabor productivity

Growth rate incapital productivity

Growth rate inreal compensation

Figure 2.1Comparative growth performance of the United States and Japan, 1965–1998.

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ductivity and the real wage move roughly in step, with the latter tendingto lag after the early 1980s (a Reagan effect?). By contrast, with just acouple of exceptions, yearly capital productivity growth in Japan wasnegative throughout the period—a rather standard observation for EastAsia. The Japanese economy avoided a FROP only insofar as its realwage tended to grow less rapidly than labor productivity.

The neoclassical approach to measuring technological change takesthe form of “sources of growth” accounting, which blends separategrowth rates of labor and capital productivity together into one term, À:

À = ψ(¼ − ü) + (1 − ψ)(¼ − ú) = ¼ − ψü − (1 − ψ)ú. (11X)

The number À emerging from these expressions is often called “total fac-tor productivity growth” (TFPG) because it is supposed to representhow overall productivity of the input factors L and K jointly rises overtime (Solow 1957). In other words, output growth ¼ is decomposed intoa weighted average of the growth rates of the inputs, ψü + (1 − ψ)ú,plus TFPG.

In much mainstream analysis À, ü, and ú are treated as predeterminedvariables so that the output growth rate ¼ is set from the side of supply.However, the accounting would be the same if ¼ were determined by ef-fective demand and À were a “residual” (another name it frequently goesby, perhaps more descriptive than TFPG). To repeat a point made previ-ously, the causal scheme to be imposed on an accounting identity like(10) requires serious thought.

Substituting À as defined in (11X) into (10) gives decompositions ofprice growth,

À = ψœ + (1 − ψ)(¹ + ¾) − ¾ = ψÛ + (1 − ψ)¹. (11P)

The expression after the first equality states that ¾ will be lower, thegreater the value of À. This productivity rein on price increases is ob-served in the data. It has to be present in a consistent accounting scheme.

The second equality, À = ψÛ + (1 − ψ)¹, is more interesting. It sup-ports a critique of the mainstream advanced by Shaikh (1974) amongothers, and elaborated by Felipe and McCombie (2002) in one of a seriesof papers. The starting point is that the value of À coming from (11X)represents a “surplus” of output growth over a weighted average of thegrowth rates of input uses. Somehow it must be distributed to actorsin the economy, and (11P) sets out the relevant accounting restriction.Trend versus cycle considerations become important in this regard.

As hinted above, the trend value of profit rate growth ¹ may be zero ornegative. However, over periods on the order of one to ten years ¹ is

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more volatile than real wage growth Û as it oscillates through the busi-ness cycle. For example, the (transient?) TFPG acceleration during thecyclical upswing in the United States in the late 1990s seemed to spillover into positive values of ¹. In general, labor productivity growth itselfappears to vary “pro” the output/distribution share cycle in the UnitedStates (see Chapter 9).

Over a longer term (decades, perhaps), if real wage growth runs atabout the same rate as labor productivity growth and there is no strongtrend in capital productivity, it will be true that À ≈ ψÛ ≈ ψ(¼ − ü), orsecular TFPG is roughly equal to the rates of real wage and productivitygrowth multiplied by the wage share.

The bottom line is that TFPG plays multiple roles. In the medium run,À in (11P) feeds into distributive conflict over the cycle. Its long-run be-havior will be driven by the technological and social forces that influencelabor productivity growth and the adjustment of the real wage thereto.Sorting out how all these factors interact in historical time is a formida-ble task. Just summing them up into an index like À and claiming it mea-sures “technological change” is not terribly helpful, despite the enor-mous effort devoted to such exercises in the decades following Solow’s1957 paper. Looking at separate trends in (¼ − ü) and (¼ − ú) à laFoley and Michl while considering concurrent shifts in the real wage andprofit rate makes more sense.

A modest step in this direction by the mainstream is to bring in “fac-tor-augmenting” technical change in the context of a production func-tion. To see how it works, we can begin with another identity,

¼ = ψ[ü + (¼ − ü)] + (1 − ψ)[ú + (¼ − ú)]. (12)

This equation basically says that ¼ = ¼ and holds for any value of ψ.However, if ψ is set equal to the labor share and rates of productivitygrowth are defined as ÀL = ¼ − ü and ÀK = ¼ − ú, it can be used forgrowth accounting in the form

¼ = ψ(ü + ÀL) + (1 − y)(ú + ÀK) = yü + (1 − ψ)ú + À. (12À)

After the first equality, output growth is decomposed into a weightedaverage of growth rates of the inputs plus their factor-augmenting ratesof technological change. After the second equality, this construct is seento boil down to TFPG. If ψ is assumed not to change over time, then(12À) is a Cobb-Douglas production function in growth rate form—a fancy reinterpretation of the identity (12) and nothing more. As il-lustrated in a moment, other production functions differ from Cobb-Douglas only in imposing auxiliary “marginal productivity” equations

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to determine ψ as some function of ω and r. The bottom line is that themainstream production function/TFPG story just adds bells and whistlesto the task of tracing changes over time in the accounting identities (10)and (12). Isn’t it more sensible to work with the identities themselves, in-stead? Attempts to do so are presented in several chapters to follow.

From the mainstream perspective, the answer to this question is “no.”Production functions and marginal productivity conditions are the wayto go. To illustrate a common neoclassical interpretation of factor aug-mentation, we can combine (12À) with the (locally) constant elasticity ofsubstitution σ. Technical change is supposed to make “effective” laborand capital inputs L* and K* grow over time according to rules such asL* = L exp(ÀLt) and K* = K exp(ÀKt). If producers still minimize costswith respect to “ordinary” input levels L and K, then it can be shown(Taylor 1979, app. D) that in log-change form demands for labor andcapital can be written as

ü = −σÛ + ¼ − (1 − σ)ÀL and ú = −σ¹ + ¼ − (1 − σ)ÀK. (13)

The effects of factor-augmentation on input demands are ambiguous;only for values of σ < 1 will positive productivity growth reduce demandfor the corresponding input. This curiosum is relevant to the discussionof “new” or “endogenous” growth theories in Chapter 11.

Setting À = ψÀL + (1 − ψ)ÀK as above, a bit of substitution shows thatequations (13) are consistent with (12) so long as one of two relation-ships (11X) and (11P) is independently valid. As already discussed insection 3, the usual neoclassical “dual” interpretation of these manipula-tions is that factor-demand equations like (13) combined with a costequation generate a production function, and vice versa. But a clearer ra-tionale is that if the decompositions in (10) or (12) fit the data (as theymust, if the numbers are constructed properly), then equations for factordemands as in (13) are the only functional forms with a single substitu-tion parameter σ that are compatible with SAM accounting. In econo-metric practice, such a one-parameter restriction is weak enough to bedifficult to refute.

Finally (setting À = 0 to concentrate on comparative statics), the log-change version of the wage-profit curve from (11P) is

ψÛ + (1 − ψ)¹ = 0. (14)

If we define u = X/K as a rough-and-ready measure of capacity utiliza-tion, then plugging (14) into the capital-demand equation in (13) andsimplifying gives the expression

Û = −[(1 − ψ)/σψ]û. (15)

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In words, the real wage is an inverse function of capacity utilization, orthe level of economic activity. The “story” is that if firms are to producemore output, they have to be presented with a lower real wage to inducethem to hire the necessary labor. Macroeconomically, this adjustment isa variation on the distributional scenario discussed in connection withTable 2.1, combining the real wage reduction of forced saving with apositive employment response.

On the other hand, labor supply may rise with the real wage, accord-ing to a (locally) constant elasticity φ: ü = φÛ. Substituting into the pro-duction function in (11X) with À = 0 gives

û = ψφÛ − ψú. (16)

In words, a higher real wage will pull more workers into the labor mar-ket. If they get jobs, the level of economic activity will rise. In the presentsetup, the invisible hand will presumably make sure that the jobs arethere, as the real wage varies to equilibrate labor supply and demand.More formally, for a given value of ú, (15) and (16) are a pair of simulta-neous equations for û and Û or for u and ω more generally. Their solu-tion determines the activity level and real wage. All this is illustrated inFigure 2.2, a diagram with axes that will become achingly familiar in thisvolume. The curves crossing in the graphs, however, will have drastically

60 chapter two

Real wageω=w/P

Labor supply

Labor demand

Output/capital ratiou X/K=

Figure 2.2Determination ofmacroeconomicequilibrium from thelabor market.

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differing contents. Labor demand and supply are the key relationships inFigure 2.2, which embodies “full employment” along the supply curve.Such an updated version of Say’s Law is congenial to many moderneconomists but alien to the visions of Kalecki and Keynes.

5. Markup Pricing in the Product Market

The major omission in Figure 2.2 is the principle of effective demand, aswill be pointed out in later chapters. A more immediate, technical point,however, is the fact that the inverse relationship between the real wageand the level of economic activity built into (15) is difficult to establishempirically. In The General Theory, Keynes went to great (some say ex-cessive) lengths to render his ideas acceptable to orthodoxy. One of hisploys was to accept the “first classical postulate” that to get higher em-ployment, labor must accept a lower real wage.12

A few years after The General Theory was published, Dunlop (1938)and Tarshis (1939) challenged this postulate empirically—if anything,real wages appeared (and, depending on how they are measured, still doappear) to vary pro-cyclically.13 In a response, Keynes (1939) had noproblem accepting this amendment to his own theory, but it remainsvexing to neoclassicists. Thereby hang many tales, some to be developedin this and the following sections. The theme they share is that it is pos-sible to replace the “new classical” or Walrasian curves in Figure 2.2with more plausible constructs, while still retaining the picture’s messagethat the macroeconomy obeys rules closely akin to the modern, full em-ployment version of Say’s Law. This message is central, for example, tothe mainstream “new Keynesian” research project that flourished in the1980s (Mankiw and Romer 1991).14 The following discussion gives ataste of new Keynesian analysis.

A basic idea is that market imperfections can generate macroeconomicrelationships resembling those of Figure 2.2, with the curves crossing ata point that determines “natural rates” of capacity utilization and em-ployment. The most obvious departure from pure competition in com-modity markets is monopoly power used to drive wedges between pricesand costs. In the simplest example, the MIRA individual is a single-mar-ket monopolist firm seeking to

Maximize PX − wbXsubject to X = X0P−η,

where the absolute value of the price elasticity of demand facing the firmis η > 1.

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Solving this problem gives a pricing rule of the form

P = wb/[1 − (1/η)] = (1 + τ)wb = wb/(1 − π). (17)

The price P is set by a margin over variable cost wb, with the markuprate τ depending on the firm’s market power as captured by the elasticityη. The cost decomposition is P = wb + πP, where π is the profit share, sothat 1 + τ = (1 − π) −1. If η tends toward infinity, price is just equal tovariable cost (P = wb), while the markup rate tends toward infinity as ηapproaches one from above.

With a constant η, we get a constant markup rate—a good first ap-proximation to what is observed. Besides monopoly power, moreover,there are numerous theoretical justifications for markup pricing. Theyinclude a desire on the part of firms to generate cash flow sufficient tofinance capital formation along forced saving lines (Eichner 1980). His-torically, stable markups provided a basis for intrafirm coordination inmultidivisional enterprises like General Motors (Semmler 1984).

But why a constant markup rate? Is there a more accurate second ap-proximation? Long ago, Pigou (1927) proposed that the markup mayvary countercyclically, contrary to the first classical postulate and forcedsaving.15 This possibility has been picked up by new Keynesians, withone suggestion being that when aggregate demand rises, novel productsenter the market (Weitzman 1982). If they substitute closely with oldones, price elasticities may increase overall, reducing markup rates fromthe first equation in (17). Another idea is that price-setting collusionamong firms may falter when demand surges (Rotemberg and Saloner1986). Third, a firm is likely to find that the proportion of new to oldcustomers in its clientele varies pro-cyclically, in a twist on the “kinkeddemand curve” explanation for markup pricing proposed by Sweezy(1939). In an attempt to lock in the loyalty of its new buyers, the firmmay shave prices (Phelps and Winter 1970).

Finally, the presence of decreasing average costs may lead to lower realprices during a boom. The two obvious candidates for lower costs perunit output are the inputs of labor and capital. Although detailed dis-cussion of the phenomenon is postponed for several later chapters, wehave already noted that labor productivity does appear to respond posi-tively to economic activity. In the short to medium run, Okun’s Law(1962) states that the elasticity of the unemployment rate with respectto U.S. GDP is about one-half (in Okun’s day, the value was more likeone-third). An earlier, longer-term analog is Verdoorn’s Law (1949) as-serting a cross-cyclical or cross-country positive relationship betweenproductivity growth and the level of output (especially in the manufac-

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turing sector). Using appropriate econometric techniques, Vernengo andBerglund (2000) find support for both relationships in U.S. time-seriesdata.

On the side of capital, costs can also shift counter-cyclically and feedinto a similarly varying markup rate. Following Hazledine (1990), thisscenario can be illustrated by a typical applied industrial organizationmodel, where N oligopolistic firms of the same size are active in a sec-tor.16 The basic idea is that firms face a fixed cost of using capital ρK(with ρ = rPK, where r is the sector’s profit rate as “required” by itsfinanciers and PK is the cost of its capital input bundle). Redefining Γ asthe average cost of production, we have

Γ = wb + ρ(K/X) = wb + [(K/N)/(X/N)] = wb + ρκ/(X/N), (18)

where κ = K/N is the industry-wide average capital stock per firm. Aver-age cost falls as output per firm X/N rises, that is, firms can “spread”their fixed capital charge ρκ over a greater volume of sales when demandswings up. In log-change form we have

ç = (1 − λ)œ + λ(Æ + Õ − ¼), (19)

where λ = ρκ(X/N)/Γ. As in the SAM of Table 1.4, the share of enterprise“operating surpluses” in value-added (or, more appropriately, the sharein the gross value of a sector’s output, which includes intermediate inputcosts) will be on the order of 0.2 or less. Fixed capital costs of the sortconsidered here necessarily appear as part of operating surpluses in thedata. Hence, the elasticity −λ of Γ with respect to X in (19) will be nega-tive but “small” in absolute value. Decreasing average cost should bevisible but not strikingly so in the sector’s time-series numbers.

The overall cost decomposition is PX = ΓX + πPX so that the pricelevel is P = (1 + τ)Γ, where the markup rate τ satisfies the relationship1 + τ = (1 − π)−1 as in (17).17 Let φ = 1 + τ be the “force” of themarkup, and assume that φ = φ0Γ−γ so that P = φΓ = φ0Γ1−γ. Here theassumption is that competition means that all cost increases cannot bepassed along into higher prices. In an economy open to competitive im-ports of goods “similar” to those produced at home, for example, γmight approximate the import share in total demand of home and for-eign goods. In an economy closed to trade, γ could be close to zero in asector without much competition.

We can also assume that new firms enter the sector when its markuprises, N = N0φµ. In a sector with relatively free entry, µ could be on theorder of ten or higher. If there are strong barriers to entry, it could be one

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or less. Finally, because new firms require investment finance, ρ may risewith the number of firms, ρ = ρ0Nβ (presumably, β is “small”).

Log-differentiating all these relationships and putting them togethergives an expression for the log-change in the sector’s price level:

¾ =1

1 1−

+ +

γ

λ β µγ( )[(1 − λ)œ − λ¼]. (20)

A nominal wage increase is passed into a higher price, although withan elasticity likely to be less than one. Higher output makes the pricelevel fall. The elasticity could be near zero for relatively large values ofthe price-cost retardation elasticity γ and the entry elasticity µ and ap-proximately equal to −λ for low values of these parameters—a counter-cyclical markup response is likely to be stronger in an economy closed tocompetitive imports and with high barriers to entry.

If such industry-level outcomes can be blown up to the economy as awhole, they suggest that the real wage ω = w/P would tend to rise in linewith increases in the both the money wage w and the level of economicactivity X. The relevant elasticities would have absolute magnitudes inthe range of 0.1 or smaller.

6. Efficiency Wages for Labor

In new Keynesian theory, markup pricing for output is often combinedwith market power with respect to labor. In a variant perhaps more rele-vant to Europe than to the United States, monopoly unions may be ableto drive up real wages when employment rises.18 The American litera-ture, by contrast, endows firms with monopsony power over their em-ployees. This position enables them to “extract labor from labor power”in Marx’s phrase, by combining wage carrots and coercion sticks to en-hance workers’ productivity and reduce shirking (Bowles and Gintis1990).

Such a labor-extraction process is often modeled with the firm as a“principal” (or Stackelberg leader) which minimizes labor cost subjectto the productivity response functions of its workers or “agents.” In atypical example, the labor-output ratio might be adjusted by workers re-acting to their perceived “cost of job loss” Z. A higher cost of being firedmeans that they would be willing to work harder. In the usual formula-tion the firm solves the following problem:

Minimize ωb(Z)subject to Z = ω − Àωa − (1− À)ωb,

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where ω is the real wage, À is the overall rate of employment (À = L/&,where & is labor supply), ωa is the wage paid by employers alternative tothe worker’s present firm, and ωb is the level of benefits paid to the unem-ployed. Because people raise their productivity when their cost of jobloss goes up, the labor-output ratio b is a decreasing function of Z.

The firm chooses ω—it is in a position to tell labor both how manyjobs will be available (given the output level X) and the level of the wage.Its optimality condition can be written out as

−Zb′/b = Z/ω = (1 − À)(ω − ωb)/ω, (21)

where ωa is set equal to ω in the substitution for Z after the second equal-ity. Toward the other end of the expression, b′ = db/dZ. Let θ stand forthe elasticity of b with respect to Z at the extreme left. Then roughlyspeaking, (21) will be satisfied for numbers such as θ = 0.475, À = 0.05,and (ω− ωb)/ω= 0.5. All these values are econometrically plausible. Forθ (locally) constant, (21) shows that a higher unemployment benefit ωb

raises the real wage ω—firms have to pay more to extract labor fromworkers if their cost of job loss falls. Aggregate demand can also affectω—there is no presumption of full employment in the efficiency wagemodel. By reducing Z at an initial level of ω, a higher employment rate Àforces firms to raise the real wage.19

7. New Keynesian Crosses and Methodological Reservations

This positive response of the real wage to the level of economic activityis central to the new Keynesian project. The narrative starts with anincrease in capacity utilization u = X/K and thereby the employmentrate À = bu(K/&), where conventionally both the capital stock K andthe available labor force & are assumed to be fixed in the short run.As we have seen, the higher value of À bids up the real wage; it also(slightly) reduces the labor/output ratio b, consistent with the Okun andVerdoorn laws. If such effects are important economy-wide, the upward-sloping “Efficiency wage” schedule in the (u, ω) plane emerges in Fig-ure 2.3.

The “Markup” schedule in the diagram draws on the model of section5, which generated a weak inverse relationship between the level of eco-nomic activity and the price/wage ratio. This linkage is captured by theshallow positive slope of the “Markup” curve. The crossing point of thecurves defines “natural” capacity utilization and real wage rates Ä and Ú,at which firms satisfy their goals with regard to both price formation andlabor extraction. If in addition money wages and prices tend to rise rela-

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tive to trend for values of u above Ä and fall under other circumstances,then (in one of the more gruesome acronyms coined by an illiterate pro-fession) the natural rate becomes a NAIRU, or “non-accelerating infla-tion rate of unemployment.”

In the American policy debate late in the 1990s and early in the dec-ade of the “aughts,” the NAIRU lost a lot of its earlier cachet becauseafter 1995 the economy was growing rapidly and operating at high lev-els of capacity utilization with little visible inflation. How this “failure”of the concept will affect its future acceptance remains to be seen. But ifwe look backward, the NAIRU had a formidably successful history;whether it was deserved or not will be thoroughly discussed in subse-quent chapters.

One reason why NAIRU-like ideas are likely to live on lies in the simi-larity between Figure 2.3 and the purely competitive, labor market-based analysis of Figure 2.2. A strength of the Figure 2.3 worldview isthat it at least admits the possibility of unemployment, because the em-ployment ratio À can be less than one. Interventions to raise À becomepossible in the form of “incomes” or incentive policies aimed at shiftingthe two schedules, as discussed by Layard, Nickell, and Jackman (1991)and Carlin and Soskice (1990). Concerted attempts to change the level ofeffective demand are bound to fail, however, because the rate of capacityutilization cannot lie above its “equilibrium” value Ä “in the long run”

66 chapter two

Real wageω = w/P

Output/capital ratiou X/K=

Efficiency wage

Markup

u

ϖ

¯

Figure 2.3Determination ofmacroeconomicequilibrium via mar-ket imperfections.

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(except possibly in the “Goldilocks economy” of the United States in thelate 1990s, when everything was “just right”).

This basic message of Figure 2.3 has been transmitted in many ways.For example, Lindbeck (1993) crosses an upward-sloping “wage-set-ting” curve with a first classical postulate labor demand function; Phelps(1994) replaces the labor demand curve with a pricing relationship froma dynamic oligopoly model. Regardless of the rationales underlying thecurves of Figure 2.3, its practical implications are hard to distinguishfrom Figure 2.2’s version of Say’s Law. Two curves originating on thesupply side cross and determine ω and u, independent of aggregate de-mand.

A final decision about the mechanism behind the curves—pure or im-pure competition—does not have to be reached at this point. However,two reasons why models based on pure competition may merit deeperconsideration are worth pointing out. One is rhetorical, the other onto-logical.

The rhetorical argument is that a fundamental critique of the capitalistsystem should be mounted on capitalism’s strongest theoretical ground,that is, perfect competition. Although their final theories were far apart,this strategy was shared by Marx and Keynes. As will be seen in Chapter4, Keynes took on the model underlying Figure 2.2 on its own terms. Byreplacing the second classical postulate with the principle of effective de-mand—reversing the Walrasian causal structure—he revoked the fullemployment statement of Say’s Law. The most powerful new classicalcounterarguments also are founded on pure competition.

By comparison, new Keynesian imperfect competition looks a bit likewindow dressing. It does not rest on the deepest foundation of The Gen-eral Theory, which as observed in Chapter 1 is a social structure involv-ing distinct roles for workers, enterprises or “business,” and rentiers.Political choice underlies the socioeconomic distinctions among these ac-tors—under modern capitalism society cedes control over productionand accumulation to corporate elites (Lindblom 1977). This decision isneither inevitable nor sacrosanct. Indeed, as Polanyi (1944) forcefullyargued, societies at times take back powers granted to the market, whenit creates such inequality or provokes such financial instability as togenerate widespread unrest. Polanyi’s view that societies move towardand away from full market liberalization in “double movements” is thebest reason to take economic analysis embodying less than perfectcompetition seriously. But Polanyi and Lindblom stand well outside ofeconomics as it is usually practiced—they are interested in society andthe state, not the latest technical tricks in modeling imperfect compe-tition.

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The ontological argument for concentrating on pure competition isalso sociopolitical, but relies on process as opposed to structure. Sim-ply put, its conclusion is that imperfect competition in all its forms—oli-gopolies, efficiency wages, externalities, indivisibilities, and so on—isdoomed to disappear in some not very lengthy run. It will be undone byentrepreneurial forces. Through entry of firms into oligopolized mar-kets, markups will be driven toward zero. Unemployed workers will toilwith high productivity at low pay to bid down efficiency wages until ev-ery willing hand finds a job. Economic externalities or production indi-visibilities will be “internalized” through bargained market solutionsuntil socially optimal marginal benefit = marginal cost equalities apply(Coase 1960).

This view of competition as a process that inevitably grinds away eco-nomic barriers because someone can make money by doing the grindingis characteristic of the Austrian school of economics, launched by CarlMenger in Vienna during the second half of the nineteenth century.20 Thebest-known latter-day Austrian is undoubtedly Friedrich von Hayek. InMilton Friedman’s heyday, the Chicago School offered a complementarysynthesis of Austrian ideas with monetarism and the perfect competitioneconomics of demand and supply.

In modern terminology, Menger and Hayek viewed the socioeconomicsystem as an evolutionary game in which the forces of entrepreneurshipwill finally prevail, leading to a socially optimal competitive resource al-location. Formally speaking, no proofs of convergence were provided.Rather, von Hayek (1988) argued that the existence and benefits of atrend toward capitalism worldwide are demonstrated by the rapid ex-pansion of the human population observed over the last few hundredyears.

There are immediate doubts. Whether modern capitalism arose spon-taneously is one question (Polanyi said it did not, stressing the role ofnineteenth-century European and American states in establishing marketsystems). Whether it is a sufficient cause of fast population growth is an-other. “Reasonable” answers tending toward the negative suggest thatarguments for the existence and convergence of Austrian entrepreneurialprocesses boil down to assertion. As it turns out, economists around theNorth Atlantic are trained to take the Austrian assertion to heart.

8. First Looks at Inflation

We will revisit queries about the durability of noncompetitive structures,for example in the theory of economic growth. But to wind up this chap-ter, one topic remains: the origins of trends in nominal prices, or in-flation.

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The initial question is which part(s) of the price system serve(s) as“nominal anchor(s),” in a recent phrase (Bruno 1993). The parenthesessuggest that the answer can be either singular or plural. There are twomain candidates.

First, the overall level of prices can be determined from the side ofcosts, along the lines of equations (2), (5), (9), (17), and so on. In thiscase, the nominal wage (so many dollars per hour) is the likely anchorfor the system—when it moves so will all other prices, more or less inproportion. In an economy open to trade (especially in the wake of veryhigh or hyperinflations which have destroyed local price relations), an-other obvious candidate is the nominal exchange rate in units of localcurrency to foreign.

Second, the money supply (billions of dollars) can anchor pricesthrough a relationship known as the “equation of exchange,” MV =PX, where M is money, P is the aggregate price index, X is real output,and V is a parameter called “velocity.” It is supposed to measure howrapidly the value of output PX “turns over” with respect to the moneysupply M. For a broad definition of “money,” Tables 1.4 and 1.5 suggestthat V for the U.S. economy is around 1.5. It would have to be approxi-mately constant for M to be able to regulate P.

These anchors are not mutually exclusive. Both could hold the pricelevel at the same time, or prices could be breaking away from both in aninflation hurricane—an event not infrequently observed. However, oneor the other of the two price-level regulators often appears to dominate,giving rise to “structuralist” and “monetarist” inflation theories respec-tively. This distinction has been around for a long time. As discussed inChapter 3, Kindleberger (1985) traces it to debates among eighteenth-century Swedes.

Inflation is unavoidably dynamic, a process of trending prices whichhas to be understood in terms of its own history, not to mention the insti-tutions and conventions of the economy in which the process is takingplace. How well do the two theories explain inflation in such terms?

The monetarist story is deceptively simple. The first approximation isthat V is constant, and the second is that it is an increasing function ofthe inflation rate ¾. The rationale is that as inflation runs faster, it erodesthe real value of the money stock more rapidly so that MIRA agents fleeto other assets; after all, the return to holding money is −¾. Differenti-ating the equation of exchange with respect to time and rearrangingshows that

d¾/dt = (V/v)(¾ + ¼ − þ), (22)

where v = dV/d¾ > 0 and the hats signify growth rates.

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Suppose that ¼ is determined by forces of supply (there is little roomfor effective demand in monetarist analysis) and that money supplygrowth þ is also predetermined (mechanisms are discussed in Chapter3). Then (22) is a differential equation giving the change of the inflationrate d¾/dt as a function of predetermined variables and the inflation rateitself. Dynamically, (22) is unstable because a higher value of ¾ increasesd¾/dt, which feeds back into a further increase in ¾. This sort of instabil-ity is characteristic of many recent macro models. The mainstream elimi-nates it by fiat. Asset holders are supposed to have perfect foresight (upto a random error term) about present and future inflation. They willavoid the instability by jumping to a perfect foresight or “rational expec-tations” inflation path along which

¾ = þ − ¼, (23)

with d¾/dt = 0 and V is constant by construction.Equation (23) is the monetarist theory of inflation: price increases are

driven by exogenous money creation. Stop “printing money,” the storygoes, and inflation will disappear. Whether such a simplistic statementcan even be approximately true in practice is a hotly debated question.21

At a more theoretical level, a couple of observations are worth making.First, like the Austrians, monetarist analysts resolve causal questions

by assertion—þ and ¼ are simply postulated to be exogenous variablesin (22) and (23). In reality, money may be created in response to risingprices or output may rise in response to money creation. There is no ob-vious way to sort out such causal links from money and price data bythemselves; outside information of an institutional or historical naturehas to be brought to bear.

Second, regardless of price trends, cost breakdowns as discussed ear-lier in this chapter continue to apply. Concretely, if ¾ is determined by þ,then nominal wage inflation œ must follow through the cost function.But it is easy to observe social processes independently affecting œ. Theyare ignored by monetarism. It cannot be a complete theory of inflation.

So how do we bring in price-cost relationships from the supply side?Social conflict over real values of input prices such as the nominal wagecan easily combine with price-propagation mechanisms such as con-tract indexation to create an inflation spiral. Conflict and propagationmechanisms are the essential elements of structuralist inflation theory.But the equation of exchange MV = PX is valid as an identity, and veloc-ity is not observed to tend to infinity (even in chronically inflationaryBrazil, the ratio of GDP to money supply only reached a level of around65 in the mid-1990s). Therefore, structuralists implicitly have to assumethat causality runs from right to left in the formula: money is “passive”

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in Olivera’s (1970) phrase. Central bankers of sufficiently inflationarymentality can easily arrange for passivity to be the rule (just as their col-leagues of deflationary inclination can revoke it).

Conflict can arise for many reasons. In the famous German hyperin-flation of the early 1920s there was tension between workers’ incomeclaims and the low real wage implicit in an exchange rate weak enoughfor the economy to be able to run a trade surplus big enough to pay theWorld War I reparations claims imposed by the Treaty of Versailles.Latin American theory after World War II emphasized low real wagesdue to high food prices. Besides “price-wage,” there can also be “wage-wage” competition. In The General Theory, Keynes stressed that differ-ent groups of workers seek to maintain their relative income positions.He was thinking of resistance to piecemeal money-wage cuts, but similarlogic applies to wage inflation. Each group will seek to have its moneywage rise at least as fast as all others.

Keynes’s insight was picked up after World War II in the United Statesby institutionalist labor economists such as Dunlop (1957). Americanlabor unions still mattered at the time, negotiating contracts that lastedfor more than one year. Each year’s round of wage increases served as atarget for the unions bargaining the following year, as the staggered con-tracts added a degree of permanence to the inflation process. WithoutDunlop’s institutionally rich description of “wage contours” across in-dustries and other social relationships, the staggered contract idea waspicked up by John Taylor (1980) in an influential new Keynesian modelof wage-wage competition as a means of propagating inflation.22 Asketch of his analysis follows, set up in discrete time to emphasize the pe-riodic nature of wage adjustments.

At time t, wages for half the workers are set, for periods t and t+ 1. Attime t + 1, wages are set for the rest of the labor force, for periods t + 1and t + 2, and so on. With labor productivity normalized to unity andno markup, algebraic simplicity dictates that the price level should be ageometric mean of wage costs,

Pt = w wt t−11 2 1 2/ / (24)

where subscripts are used to denote time periods.Velocity is also conveniently equal to one, so that in a transformation

of the equation of exchange from a description of asset preferences intoan effective demand curve (a sleight of hand discussed at length in subse-quent chapters), output Xt is given by

Xt = Mt/Pt, (25)

where Mt is the money supply at time t.

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In standard Cobb-Douglas or “log-linear” form, Taylor assumes thatwages at time t are determined in response to last period’s observed levelwt-1 and the level expected next period, wt+1, along with positive effectsof current and future demand Xt and Xt+1,23

wt = [wt−1Xtγ ]β[wt+1Xt+1

γ ]1−β. (26)

The parameter β indicates whether wage adjustment looks backward (β= 1 in the extreme case) or forward (β → 0). It is argued below on insti-tutional grounds that β = 1 is more likely, but in much discussion β is setto 1/2. The elasticity γ measures the strength of the demand boost towage claims.

Plugging (24) and (25) into (26) and going through some algebra givethe relationship

1 = (M Mt tβ β

+−1

1 )φ-1w w wt t t−−

+−

1 11β φ β , (27)

where φ = [1 + (1/2)γ]/[1 − (1/2)γ] > 1. This formula shows how wagelevels have to adjust over time to satisfy the indexing rule (26). As itturns out, the equation is satisfied by a wage adjustment of the form wt+1

= wtα , where α > 1 signifies wage growth over time. To solve for α, one

can take logs in (27) to get

0 = β + (φ − 1)[β log(Mt) + (1 − β)log(Mt+1)]/log(wt−1)− φα + (1 − β)α2.

Since φ > 1, the solution of this quadratic equation in α that can permitstable wages (or α = 1) takes the form

αφ φ β β µ

β=

− − − +

[ ( )( )]( )

/2 1 24 12 1

(28)

in which µ = (φ − 1)[β log(Mt) + (1 − β)log(Mt+1]/log(wt−1)].The α= 1 stability condition implies that µ= φ− 1 or [M Mt t

β β−−1

1 ]γ/wt−1

= 1. Suppose this equality is satisfied but that Mt unexpectedly jumpsupward. In (28) µ will increase, driving up α and making wt exceed thelevel wt−1 it would have had with Mt unchanged. From (24), the pricelevel Pt will increase by less than the money supply, and from (25) aggre-gate demand will rise. Output, the price level, and wages will remainabove their initial levels in subsequent periods, only converging back towhere they began as higher wages gradually reduce µ over time. Persis-tent inflationary and expansionary effects of the monetary shock arebuilt into the dynamics by staggered contract indexation. This linkagehas emerged as a repeated theme in new Keynesian analyses of inflation.

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Despite sporadic attempts at forward indexation (β → 0 in Taylor’sformulation), in practice wage adjustment schemes are almost alwaysbackward-looking, because contrary to much recent economic theoriz-ing, union leaders and business people are not blessed with perfect fore-sight about future price and output changes. We can illustrate how in-dexation interacts with social conflict in a simple model incorporatingadjustment periods that can change. Shortening or increasing the timespan between price and wage revisions is a policy issue that has been im-portant in many inflationary economies over the past few decades. Thebasis for the discussion is a corrected version of an early model for Italy,worked out by Modigliani and Padoa-Schioppa (1978).24

Prices in period t are assumed to be set according to the laggedmarkup rule

Pt = h(1 + τ)wtb + (1 − h)Pt−1, (29)

where a fraction h of current wage cost wtb is passed into prices via themarkup at rate τ. The lagged price Pt−1 feeds into the current level with acoefficient 1 − h.

Wages are fully indexed between periods according to the formula

wt = ÚPt−1, (30)

where Ú stands for a highest instantaneous real wage that workers get.At the beginning of period t, wt is set according to (30), and then real la-bor income erodes as prices rise during the period (a year, a quarter, orperhaps even less). Avoiding wage erosion is the workers’ game in thismodel—the details come shortly.

The price inflation rate ¾t coming from (29) and (30) is

¾t = [(Pt − Pt−1)/Pt−1] = h[(1 + τ)Úb − 1] = hF, (31)

so that inflation runs at a steady rate when F > 0, that is, when desiredmarkup and peak real wage claims conflict. On the demand side of theeconomy there must be some mechanism to ration output among theconflicting groups. Forced saving would serve, as would the “inflationtax” implicit in the flight from money discussed above in connectionwith the equation of exchange.

Equation (31) shows that ¾t will be larger, the more rapidly wage costsare marked up according to the coefficient h. For the non-Pigovian (butconventional) case in which the markup rate increases with capacity uti-lization, the model is illustrated in Figure 2.4. There will be inflation atany utilization level u exceeding Ä. Moreover, one can show that wt/Pt =

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Ú/(1 + ¾t), so the real wage that workers actually get at the point of in-dexation is lower as inflation runs faster.

When trending prices settle in, history in Latin America and other in-flationary corners of the world demonstrates that pressures to shortenindexation periods always develop. With an annual rate of up to 30 per-cent (say), workers may accept yearly readjustment, but if inflation ismuch more rapid, they are likely to press for semiannual or quarterlycontracts. At 100 percent per year (just under 6 percent per month),monthly readjustments may come into play. The analytical question is:what is the impact of shortening indexation intervals on the inflationrate? Our first major conclusion is that more frequent indexation maywell make inflation speed up.

Suppose that suddenly the rules are changed so that there are N index-ation periods per year instead of just one (from now on we use t and t −1 to stand for the end and beginning of a year respectively). A point ofreference for the pricing behavior of firms is the new inflation pass-through coefficient hN that would hold the annual inflation rate con-stant. With an indexation period of one year, (31) can be restated asP1/P0 = hF + 1. The analogous formula for N indexation periods peryear is PN/P0 = (hNF + 1)N. Setting PN = P1 it is easy to solve for hN interms of h, that is,

hN = (1/F)[(hF + 1)ξ − 1], (32)

74 chapter two

Price/wageratio

Output/capital ratiou X/K=

u

(1 + )bτ

ω1/

u

Figure 2.4Conflicting claimswith price and wageindexation.

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where ξ = 1/N is the length of the new period of indexation. Experimen-tation shows that the value of hN from (31) is a little bit less than h/N.

If annual inflation stays constant when the pass-through coefficientshifts from h to hN, what happens if it is set to h/N (an easier adjustmentfor firms) or simply doesn’t move? Table 2.2 provides some illustrativeanswers with F = 0.3.

The moral of these numbers is that inflation rates can be highly unsta-ble in an upward direction if firms do not modify their pricing behaviorto conform to the new indexation rules. Even if they make the “obvious”h → h/N adjustment, inflation can inch up with indexation, and it caneasily take off if h is not changed or only adjusted slightly downward,

To pursue the discussion further, we set aside markup dynamics forthe moment to ask how the peak real wage Ú in (30) in fact gets set. Tothat end, let ω stand for the average real wage over the indexation pe-riod. Figure 2.5 is a diagram familiar in inflation-prone countries, show-ing how ω oscillates under an indexation scheme in which wages are re-adjusted every ξ units of time. If λ = ξ/2 and inflation is steady, then ω isgiven (approximately) by the formula

ω = Ú(Pt−λ/Pt) (33)

while the annual inflation rate is

Z = (Ú/ω)1/λ − 1. (34)

Finally, suppressing institutional detail, historical discontinuity, and par-tial irreversibility in one blow, we can assume the indexation period isdetermined according to a simple rule of the form

λ = λ0/(1 + Z). (35)

Lying behind the real wage peak Ú is a target real wage ω* that work-ers wish to receive. This target in fact will evolve over time in light ofchanging bargaining positions, the employment situation, government

prices and distribution 75

Table 2.2 Responses of the inflation rate to more rapid wage indexations.

Annual inflation rate for an initial value of h

Number of wageadjustments

per year

h = 0.5 h = 0.8

h unchanged h → h/N h unchanged h → h/N

1 0.15 0.15 0.24 0.242 0.32 0.155 0.54 0.2544 0.75 0.159 1.36 0.262

12 4.35 0.162 12.21 0.269

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policy, and many other factors. But to illustrate what happens when ω*is stable in the short to medium run, we can start from a nonconflict situ-ation in which there is ongoing inflation but the wage target has in factbeen attained between times t− 2ξ and t− ξ, as illustrated in Figure 2.6.

Suppose that there is a crop failure, devaluation, or some other suchshock at t − ξ. Inflation accelerates during the next period, and the aver-age real wage falls below its previous (and target) level ω*. Workers re-spond with increased money-wage claims, pressing for an increase in thepeak from its old level Út−ξ to a new level Út. Following Ros (1988), wecan say that “inertial inflation” describes the situation in which they suc-ceed. The peak wage moves upward to allow workers to recover the tar-get in the period between t and t + ξ. They suffer only a one-period,transitional real income loss as inflation accelerates. There is inertia inthe sense that when steady inflation returns, workers regain 100 percentindexation at their target real wage.

The problem with this scenario is that it ignores both markup dynam-ics and potential shortening of the indexing period coupled with incom-plete adjustment of their inflation pass-through coefficient by firms. Bothfactors are likely to provoke a new jump in the inflation rate, with subse-quent adjustment of the wage peak Ú, another upward movement in theinflation rate, and so on. As stressed by Amadeo (1994) and many otherauthors, this situation is unstable in the sense that any adverse price de-

76 chapter two

Real wageω = w/P

Time

ω

ξ ξ

ϖ

Figure 2.5Real wage fluctua-tions under inflation.

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velopment, originating for example in supply-limited “flex-price” sec-tors or foreign trade, can easily provoke price increases to speed up.

This general conclusion also applies to “heterodox shock” anti-infla-tion packages which attempt to stop the process by combining pricefreezes with contract de-indexation. Their goal is to eliminate the infla-tion spiral by freezing prices and wages and de-indexing contracts at astroke. Unfortunately, there are likely to be unfavorable demand effectsfrom the shock and balance-of-payments complications as well (Taylor1994).25 The policy conclusion is that even if inflation is inertial, it can-not be attacked solely from the side of costs. Contract de-indexationmay be a necessary condition for stopping inflation, but other policieshave to be applied as well. And beyond “policy” in the usual sense of theword, unless conflicting income claims are ameliorated inflation is likelyto recur.

“Conflict inflation” can be said to occur when workers’ aspirations inFigure 2.6 are not fulfilled. The wage peak is increased less than propor-tionately to the real wage loss between times t − ξ and t; hence workers’real income losses persist. Suppose that they resort to pressing for ashorter indexation period along the lines of (35). One possible outcomeis an indexation spiral as illustrated in Figure 2.7.

The “Wage inflation” schedule in the diagram represents (34), and the“Indexing rule” is (35); the curves can intersect twice. The lower equilib-rium at point A is stable while B is unstable. At B, an inflationary shock

prices and distribution 77

Real wageϖ = w/P

Time

ω*

ϖt

ϖt−ξ

t − 2ξ t − 2ξ t

Figure 2.6Adjustment of thepeak real wage to ac-celeration in inflation.

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leads Zt to rise, provoking a large increase in the indexation frequencyN, another upward jump in inflation, and so on. Such a divergent pro-cess is often invoked in structuralist analyses of hyperinflations such asGermany’s after World War I (Franco 1986). If, because of an upwardjump in the peak wage or an increase in the overall frequency of index-ation, the Wage inflation schedule lies completely above the Indexingrule, not even the unstable equilibrium at B can exist.

This interpretation of Figure 2.7 here is structuralist, but there areorthodox versions as well. The government may incur so much debt thatit outstrips the market’s willingness to lend in a “debt trap” (Chapter 6)or emit so much money that it overwhelms the resource-mobilizing ca-pabilities of the inflation tax (Chapter 3). An alarmist diagram like Fig-ure 2.7 has many incarnations; some, like hyperinflation, can even occurin practice.

78 chapter two

B

A

Inflationrate

Frequency ofindexation

Indexingrule

Wageinflation

Figure 2.7Interaction betweenconflict inflation andthe frequency of in-dexation.

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chapter three

z

Money, Interest, and Inflation

This chapter continues our discussion of “macro” price theory. Follow-ing on from Chapter 2’s sketch of the monetarist/structuralist inflationdebate, it begins with a review of the different visions that economistshave developed over a couple of centuries about the interactions ofmoney, interest, and prices. The next topics are diverse theories of the in-terest rate: its role as a component of cost; its interpretation as a relativeprice between present utility and future production in Irving Fisher’s“real” formulation (which influenced Keynes); and then fairly completepresentations of the Ramsey optimal saving and overlapping generationsmodels, which are the frameworks for most current mainstream macro-economics. The chapter continues with a formal statement of Wicksell’scumulative process inflation model based on a “natural” rate of interest.With its effective demand implications, Wicksell’s model is a steppingstone to The General Theory. One of its major components is an “infla-tion tax” on money balances. We close with a quick look at some of thetax’s applications, post-Wicksell.

1. Money and Credit

How does money affect macroeconomic equilibrium? This question hasbeen hotly debated among economists and more sensible people sincebefore 1750. It can be posed from at least three angles:

First, does money largely control, or just respond to, developmentselsewhere in the economy? Is money “active” (exogenous and de-termined prior to other variables) or “passive” (endogenous) as instructuralist inflation theory?

Second, do changes in the money supply mostly affect the volume ofactivity, or the price level? What are the channels via which moneyhas its impacts on quantities and prices?

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Third, should we concentrate analysis on changes in “money” (bank-ing system liabilities) or “credit” (banking system assets)?

Over the long sweep of economic analysis, one can find eminent parti-sans of all eight analytical positions implicit in this three-way classifica-tion. Table 3.1 presents an outline. We will go through the entries tosketch informally the theoretical views underlying each cell, roughly inchronological order.1 Lessons for subsequent analysis will also be drawn.

Early participants in the matrix include two political parties—the“Hats” and the “Caps”—that appear in the active/quantities/credit andactive/prices/credit slots. They flourished in a parliamentary democracyfor a few decades between Divine Right despots in Sweden in the mid-eighteenth century. As their names suggest, the parties represented thebig and small merchant bourgeoisie respectively. These rather obscurehistorical groupings are of interest because the Hats and Caps were thefirst proponents of distinctively “structuralist” and “monetarist” posi-tions in macro theory (Kindleberger 1985).

The Hats were policy activists, urging credit creation to spur the Baltictrade. The Caps countered with arguments that excessive spending couldlead to inflation, payments deficits, and related ills. The Hats took powerafter a period of slow Cap growth and (as often happens with expan-sionist parties) pushed too hard—they lost power in an inflation and for-eign exchange crisis in 1765. Despite their respective policy failures, theintellectual points raised by the politically warring Swedes carry downthrough the years.

80 chapter three

Table 3.1 Positions of different monetary analysts.

Main effects of money/credit

Causal status ofmoney/credit

On prices On quantities

Via money Via credit Via money Via credit

Passive Hume Thornton Malthus MarxWicksell Banking KaldorSchumpeter School Minsky

Real BusinessCycle School

Active Ricardo “Caps” Keynes “Hats”Currency Law

SchoolMillMonetarists

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Both parties were fundamentally mercantilist. Had they stooped to al-gebra, they might have summarized their basic macro model as

J = I + B = J(interest rate, credit)S = S(population, unemployment, real wage)J − S = 0

where J stands for demand injections (investment I and the trade surplusB) and S represents saving leakages. Various policy instruments and so-cial processes could regulate the variables in the equations, namely, Mal-thusian checks for population, the poorhouse for unemployment, forcedsaving for the real wage, and tariffs and export subsidies for trade bal-ance.

Investment could be spurred by low interest rates ensured by usurylaws or credit creation. The importance of credit was stressed by JohnLaw, a Scotsman who sought to stimulate French growth early in theeighteenth century by setting up development banks. That his schemeled to the Mississippi Bubble—one of the earliest speculative booms—has echoes in the financial instability theories of Hyman Minsky (1975,1986), a contemporary economist who also emphasizes that banks ac-tively create credit which can have a strong influence on output via“Keynesian” channels. As will be seen in Chapter 8, moreover, financialinnovations help make this credit expansion an endogenous variable inthe overall macro system. Minskyan feedbacks between real output andexpansionary finance can be so strong as to lead to macro instability.John Law’s fortunes might have fared better had perfect foresight en-abled him to grasp what his distant analytical descendent Minsky hadto say.

Caps, Hats, and Law all argued as if money and credit could be con-trolled by the relevant authorities. Part of the intellectual reactionagainst mercantilism took the form of making money (or “specie”) aswell as the trade surplus endogenous in the short run. David Hume(1969), a world-class philosopher turning into a best-selling historiancirca 1750, is usually credited with this advance in economic analysis. Itsimplications will figure in Chapter 10 on open economy macro.

Hume’s location in the passive/prices/money slot follows from a modelthat might be written as

D = D(M/P)X = X(employment)MV = PX = X − D(X/V) = B(P*/P)

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As in John Taylor’s inflation model discussed in the last chapter, aggre-gate demand D depends on the real money stock M/P while (assum-ing full employment) output X is predetermined. The expansion in themoney supply (= dM/dt) is given by specie inflow resulting from thetrade surplus B = X − D—in this sense money is passive or endogenous.Because money drives the price level P via the equation of exchange,money expansion is an inverse function of P and thereby of M itself.The last expression for normalizes this response around a “world”price P*. The stable dynamics here contrasts sharply with the unstablemonetarist inflation process discussed toward the end of both Chapter 2and this chapter. Open-economy monetarism is a beast rather differentfrom its closed-economy cousin.

The behavioral story is simple, and well known. A big money stockmeans that there is a high domestic price level and excess demand. Thetrade surplus becomes negative when D is high, forcing specie to flowout of the country and prices to fall. Aggregate demand ceases to draw inimports, and “our” exports sell better—the trade deficit declines towardequilibrium. Policymakers’ attempts to stimulate output by monetaryexpansion (say, by raising the banking system’s money/specie multiplier)will backfire in this model; their attempt will just drive up prices andworsen the trade deficit. Although they reasoned on different groundsand far less cogently, the Caps would have approved of this conclusion.The same is true of contemporary exponents of policy ineffectivenessdiscussed in several subsequent chapters.

The next major players in Table 3.1 are Malthus and Ricardo, whostand opposed in the northeast and southwest corners. We have alreadyseen that the former argued along proto-Keynesian lines that food pricesshould be kept high by import restrictions, so that landlords (notori-ously low savers) would spend on luxuries to support industrial demand.A precursor of the structuralist Banking School, Malthus thought thatthe money supply and/or velocity adjusted endogenously to meet de-mand, or the “needs of trade.”

Ricardo, a superb monetary theorist, differed from Malthus in accept-ing supply-side determination of output, the nineteenth-century versionof Say’s Law. He naturally followed the monetarist trail, most notably in1810 when he attacked “excessive” British note issue to finance the waragainst Napoleon. His evidence included a premium on gold in terms ofnotes within Britain, and a fall of the exchange value of sterling in Ham-burg and Amsterdam. His logic was based on the quantity theory andpurchasing power parity—standard components of all subsequent open-economy monetarist models.

Ricardo’s main policy recommendation was a Friedmanite rule called

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the “currency principle,” recommending that the outstanding moneystock should be strictly tied to gold reserves. Money should not be cre-ated for frivolous pursuits such as combating tyranny, and its supplyshould only be allowed to fluctuate in response to movements of gold. Ineffect, Ricardo sought to steer monetary policy along the trail blazed byHume.

The Currency School, which took the monetarist side in British finan-cial debates well into the nineteenth century, was founded on Ricardo’sprinciple. Its great victory was Peel’s Charter Act of 1844 for the Bank ofEngland, which put a limit on the issue of notes against securities. Abovethe limit, notes had to be backed by gold. This triumph of principle overpractice was short-lived, since there was a run against English banks in1847. The Bank of England acted (correctly) as what the many-sidedWalter Bagehot ([1873] 1962)—the defining editor of the Economistmagazine—in the 1870s christened a “lender of last resort.” It pumpedresources into commercial banks in danger of collapse. To this end,the Charter Act had to be suspended. As will be seen in Chapters 9 and10, in its essentials this financial instability scenario remains unchangedtoday.

As the Currency School flourished, John Stuart Mill was putting to-gether his own economic synthesis. Although he had some sympathy forthe Banking School (see below), Mill is placed in the active/prices/moneyslot because he codified the doctrine of “loanable funds” which un-derlies much subsequent mainstream thought as discussed later in thischapter. Following Henry Thornton, a contemporary of Ricardo, Millthought the interest rate would adjust to erase any difference betweenaggregate saving and investment, thereby clearing the market for loan-able funds. As already observed in Chapter 2, this theory undergirdsSay’s Law by bringing in changes in the interest rate to ensure full em-ployment investment-savings balance.

Loanable funds is a nonmonetary theory of the rate of interest, of thesort later criticized by Keynes (see Chapter 4). It incorporates Patinkin’s(1966) “dichotomy” in that money can affect only the price (and pre-sumably the wage) level, without any influence on the volume of produc-tion. This is the ultimate monetarist position, with echoes in both IrvingFisher’s suggestion that monetary policy should be actively deployed tocontrol prices and Milton Friedman’s argument against active policy (be-cause its effects on output only are visible with “long and variable lags”while money rules the price level best in the long run).

The final entries in the broadly monetarist left columns of Table 3.1are Thornton, Knut Wicksell, and Schumpeter (with respect to the short-run macro adjustment scenario in his Theory of Economic Develop-

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ment, at least) in the passive/prices/credit niche. Schumpeter’s visiontranscends mere monetary analysis; for purposes of later discussion, itmakes sense to present an outline here.

Schumpeter took over much of Marx’s emphasis on the importance oftechnical change in generating supply and combined it with a provoca-tive analysis of how the economy responds to such innovation in forg-ing his own defense of capitalism—he called his teacher Böhm-Bawerk(to be discussed presently) a “bourgeois Marx” but could have appliedthe label equally to himself. His theories are also very Keynesian (orWicksellian) in building the growth process around the supply of creditand making macro adjustments to changes in investment demand.

The starting point is rather like the mainstream’s Walrasian models ofsteady growth, which Schumpeter calls “circular flow.” An economy incircular flow may be expanding, but it is not “developing” in his termi-nology. Development occurs only when an entrepreneur makes an inno-vation—a new technique, product, or way of organizing things—andshifts production coefficients or the rules of the game. He gains a mo-nopoly profit until other people catch on and imitate, and the economymoves to a new configuration of circular flow.

The invention or insight underlying the innovation need not be the en-trepreneur’s—Schumpeter’s “new man” simply seizes it, puts it in action,makes his money, and (more likely than not) passes into the aristocracyas he retires. Ultimately, his innovation and fortune will be supplantedby others in the process of “creative destruction” that makes capitalisteconomies progress.

The key analytical question about this process refers to both the finan-cial and the real sides of the economy—how does the entrepreneur ob-tain resources to innovate? An endogenous money supply and redistri-bution of real income flows are required to support his efforts.

To get his project going, the entrepreneur must invest—an extra de-mand imposed upon an economy already using its resources fully in cir-cular flow. To finance investment, he obtains loans from the banks; newcredit and thereby money are created in the process. The bank loans areused to purchase goods in momentarily fixed supply. Their prices aredriven up, so that real incomes of other economic actors decline. Themost common examples are workers receiving temporarily fixed nomi-nal wages or the cash flows of noninnovating firms. There is forced sav-ing along the lines discussed in Chapter 2 as workers’ lower real incomesforce them to consume less; groups which receive windfall income gainsare implicitly assumed to have higher saving propensities so that overallaggregate demand declines. Meanwhile, routine investment projects maybe cut back.

The transition between states of circular flow is demand driven from

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the investment side (though, of course, the innovation may involve pro-duction of new goods or increases in productivity) and short-run macroadjustment takes place through income redistribution via forced savingwith an endogenously varying money supply. The Walrasian “marginalthis equals marginal that” resource allocation rules that reign in circularflow are necessarily ruptured by the price changes underlying redistribu-tion (a point that Kaldor (1956) later emphasized in his discussion of dis-tribution). In a longer run, there can be a cyclical depression due to“autodeflation” as bank loans are repaid; workers can regain real in-come via falling costs. In later versions of the model, Schumpeter empha-sized that bankruptcy of outdated firms can also release resources for in-novators, but the essentials are the same.

A very similar macro adjustment story appears in Wicksell (1935), al-though much of his analysis was anticipated by Thornton almost onehundred years before. We have already noted that the Keynes of theTreatise on Money (1930) was a stalwart post-Wicksellian along withSchumpeter. Only his revised views in The General Theory (1936) placehim in the active/quantities/money cell.

Wicksell extended loanable funds theory by proposing that inflation isa “cumulative process” based on the discrepancy between new credit de-manded by investors and new deposit supply from desired saving (corre-sponding to a zero rate of inflation) at a rate of interest fixed by thebanks. Anticipating the formal model of section 8, it is worthwhile nowto talk through the cumulative process, by way of introduction.

Suppose that the banks set the interest rate too low. Then an excessof new credits over new deposits leads to money creation; via the equa-tion of exchange at presumed full employment, the consequence is ris-ing prices. Inflation is the outcome of endogenous monetary emission,driven by credit creation.

The key analytical question is how saving and investment are broughttogether to secure macroeconomic equilibrium ex post. Forced savingcan provide part of the adjustment, if wages are incompletely indexed toprice increases. The rest comes from the “inflation tax,” a dynamic ver-sion of the well-known “real balance effect,” which states that people in-crease their saving to restore the real value of their money stock M/Pwhich is squeezed when P rises. To keep to essentials, let output X and(temporarily) velocity V be constant in the equation of exchange MV =PX. The inflation tax interpretation rests on the equations

/PX = ¯(M/P)/PX = ¾/V,

which follow from the growth rate version of the equation of exchange,þ = ¾. After the first equality, ¯(M/P) is the instantaneous loss in real

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balances from price increases ¯, which wealth-holders are supposed tomake good by extra saving so that the “tax” effectively cuts aggregatedemand. The expression after the second equality shows that the taxbase erodes if V rises when inflation speeds up (the monetarists’ favoritestylized fact).

Wicksell thought that after a time, bankers would raise the interestrate to its “natural” level to bring the cumulative inflation to a halt, butfor present purposes this ending is not essential to his story. The keypoint is that through both the inflation tax and forced saving, a risingprice level liquidates ex ante excess aggregate demand. This model is theclearest monetarist alternative to the structuralist inflation theories al-ready discussed.

Returning attention to Table 3.1, the next point of interest is the pas-sive/quantities/money Banking School, the main rival of the CurrencySchool in last century’s British debate. The group is famous (or notori-ous, depending on one’s perspective) for espousing the doctrine of “realbills.” In the early nineteenth century, the banking system devoted mostof its efforts to accepting (at a discount) paper issued by merchants inpursuit of trade. The Banking School’s doctrine stated that the banksshould discount all solid, nonspeculative commercial paper, that is, trueor real debts. How in practice a banker should identify paper tied firmlyto the needs of trade was not spelled out; indeed Adam Smith (an earlyproponent of the doctrine) advised that banks should concentrate onreal trade to avoid ratifying currency speculation.

Extreme members of the Banking School finessed Smithian fears witha “law of reflux” through which excessive lending would drive up activ-ity and/or prices and lead the private sector to pay off loans and buygold: there would be an automatic contraction of the money supply inresponse to too aggressive attempts to expand it. Hume’s policy irrele-vance reappears in structuralist guise, albeit without his specie flow con-siderations.

Real bills ideas have downside implications as well. If credit needs arenot satisfied by banks, then new, nonbank financial instruments arelikely to be invented to meet the needs of trade (Minsky puts a lot of em-phasis on this sort of financial innovation). Such a Coase (1960)-styleoutcome sometimes happens, sometimes not, but it is implicit in BankingSchool views. Among structuralists, reflux notions show up in the 1959report on the British monetary system by the Radcliffe Committee and inKaldor (1982). The latter is worth quoting: “If . . . more money comesinto existence than the public, at the given or expected level of incomesor expenditures, wishes to hold, the excess will be automatically extin-guished—either through debt repayment or its conversion into interest-

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bearing assets.” One notes a certain affinity in structuralist positionsacross 150 years.

The final entries in the matrix are the Real Business Cycle School andMarx, perhaps demonstrating that economic perceptions can unitestrange political bedfellows. The former group is a recent offshoot ofnew classical economics, at the mainstream’s Walrasian verge extreme asdiscussed in Chapter 6. Its members argue that business cycles in ad-vanced economies are due to strong substitution responses (labor versusleisure choices, and so on) to supply-side shocks to the macro system.They deem money unimportant and subject to “reverse causality.” Theyare joined by Kaldor and the post-Keynesians Davidson and Weintraub(1973) in their view that typical Central Bank responsiveness to tradeplus the presence of inside money render monetary aggregates endoge-nous: their leads and lags with output depend on institutions and contin-gencies beyond the analytical reach of Granger-Sims causality tests andsimilar econometric probes.

Marx, as always, is more complex. The existence of money was cen-tral to his view of capitalism, incarnated in the famous M − C − M′ se-quence, in which exploitation arises as money M is thrown into circula-tion of commodities C (incorporating labor power and the means ofproduction), which yields a money return M′: surplus value is M′ − M.Access to M gives capitalists a leg up in the economy, making their ex-traction of surplus possible. At a more applied level of abstraction, Marxroughly adhered to Banking School ideas, at times arguing that velocityvaries to satisfy the equation of exchange. This view is consistent withthe endogeneity of inside money, for example, financial obligations cre-ated and destroyed by transactions among firms. Building on the repro-duction schemes in Volume II of Capital, Foley (1986) extended thisapproach to set up real/financial “circuit of capital” models in which en-dogenous fluctuations can occur.

2. Diverse Interest Theories

If we turn to the interest rate per se, an initial observation is that it verywell may be a price, but the price of what? The answer has changed overtime. Classical economists through Marx largely treated interest as a cat-egory within the general flow of surplus (along the lines of Chapter 2, theportion of the gross value of production not devoted to purchases of la-bor services or intermediate inputs). Interest payments were just anothertransaction among capitalists. There are vestiges of this perspective ingrowth models such as the famous one by Pasinetti (1962). He postu-lates two classes of income recipients—rentiers and workers. The latter

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receive a share of total profits (perhaps proportional to the profit rate),which authors following Laing (1969) call “interest.” To a certain ex-tent, this line of thought is pursued in later chapters with models inwhich different economic classes hold diverse portfolios of financial as-sets with differential rates of return.

The interest rate could also be the price of holding nonfinancial assetssuch as the vehicles lined up neatly in a car dealer’s lot. Business peoplethink so, and in the following section we trace through the implicationsof treating interest payments as a component of cost.2 Most economists,however, prefer to think of interest as a payment for deferred gratifica-tion and/or the possibility of making higher profits in years to come. Thisinterpretation of the interest rate as a relative price mediating transac-tions between the present and future is built into “real” theories such asthose constructed early in the past century by Irving Fisher and FrankRamsey, among many others.

As already noted, Fisher influenced Keynes, while Ramsey’s optimalsaving model (along with its “overlapping generations” analog) domi-nates contemporary mainstream thought. Applied in practice, real theo-ries tend to treat the interest rate as the variable which adjusts to clearthe market for loanable funds, as in the teachings of J. S. Mill. Loanablefunds interest rate models contrast with the “liquidity preference” the-ory developed by the Keynes of The General Theory (to be reviewedin the following chapter). Keynes’s “monetary” analysis dominated themainstream for a few decades. But it has been eclipsed by the real andloanable funds models presently in vogue.

3. Interest Rate Cost-Push

Regardless of how the interest rate is determined, a model developed byAnyadike-Danes, Coutts, and Godley (1988) provides a framework fortreating it as a cost that enterprises have to pay to hold inventories—auseful point with which to begin our discussion. To see the details, wecan write out a modified version of the cost and sales decompositions ap-pearing in column (1) and row (A) of Table 1.2’s SAM:3

wbX + πPX + iL = P(C + I + G) + P‰ + ¯Z. (1)

The notation is familiar, except that Z stands for the stock of inventoriesheld by firms and the value of investment PI does not include changes ininventories, which are represented by the term P‰. The profit share πshould be figured net of interest payments and i is a nominal or moneyrate of interest as determined in the market.

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There are two nonstandard features in the income-expenditure state-ment (1). First, the interest bill on a volume of loans L at rate i that enter-prises pay is treated as a component of cost and not as a transfer. Second,the capital gain (or loss) ¯Z on inventories appears on the right-handside. The rationale is that stocks turn over “within” the accountingperiod, so that firms have to adjust outlays to compensate for pricechanges.

Suppose that firms take loans to finance inventory: L = PZ. Let Xstand for output, as usual: X = C + I + G + ‰. Finally, assume that in-ventory is held in proportion to output: Z = ξX (Tables 1.4 and 1.6 sug-gest that the ratio of the stock of inventories to GDP is about 0.15).Plugging these hypotheses into (1) and simplifying gives the pricing rule

P =wb

i1− − −π ξ( $P). (2)

In words, the price level is formed as a markup on wage cost, with themarkup rate increasing as a function of the profit share π and the real in-terest cost (i − ¾)ξ of financing inventory. The partial derivative of Pwith respect to i − ¾ is equal to Pξ/ψ, where ψ is the labor share. With Pnormalized to one initially, the implication is that an increase in the in-terest rate of 1 percent might raise the price level by, say, [0.15/0.75]% =0.2%—a nontrivial impact.

The notion that the price level (and, by extension, the inflation rate)depends positively on the interest rate has a checkered history. It flies inthe face of conventional wisdom. Suppose that a NAIRU exists, and thatas the activity level strays above it inflation speeds up. A central bank in-tervention to raise the interest rate and cut aggregate demand is alwaysproposed as the remedy of choice. The higher cost of borrowing is sup-posed to brake rising prices. But the remedy can fail when an equationlike (2) applies, especially with a high value of ξ and a low wage share(more characteristic of developing than industrialized economies).

An early opponent of tight money was Thomas Tooke, a foundingmember of the Banking School who wrote an influential History ofPrices. A century later in his Treatise, Keynes (1930) labeled the positiveinterest rate/price level correlation that Tooke emphasized (and whichmany others have observed) the “Gibson paradox.” He and Wicksell ex-plained it away on the grounds that the money rate of interest lags thebusiness cycle.

Despite this impressive weight of authority against it, interest ratecost-push continues to appeal to both business people and expansion-ist economists. In the United States it is sometimes called the “Wright

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Patman effect” in honor of an easy-money Texas congressman whojousted with the Federal Reserve in the 1950s. The current Latin Ameri-can label is the “Cavallo effect” (1977) after the Argentine minister ofeconomy of the 1990s who found empirical support for the phenome-non in his Harvard Ph.D. thesis. He later found it politic to repudiate thedoctrine. Perhaps surprisingly, at about the same time the arch–new clas-sical economists Sargent and Wallace (1981) came up with another argu-ment tying tighter money (though not higher interest rates) to faster in-flation. Details in section 9 below.

4. Real Interest Rate Theory

The role of the real interest rate as a relative price between present andfuture economic choices was stressed by many of the founders of neo-classical economics, especially the Austrian School; members of theschool placed great weight on the roundabout nature of production.Their definitive statement came in the late 1800s from Eugen von Böhm-Bawerk, who also made a name for himself as finance minister, for criti-cizing Marx, and for being Schumpeter’s thesis advisor. He proposedthree reasons for the existence of a nonzero real rate of interest.

The first was “different circumstances of want and provision” in pres-ent and future, with one example being different income levels that affectthe marginal utility of consumption (in more modern jargon). Secondcame “underestimation of the future,” or pure time preference. Finally,we get technical differences between the present and future, for example,more or less roundaboutness. These three reasons all fit into contempo-rary optimal savings models, as discussed in the following section.

Before getting into that, however, it makes sense to sketch the fullestelaboration of Böhm-Bawerk’s own ideas, in models presented in finalform by the Yale economist Irving Fisher (1930) after a maturation pe-riod of several decades. One took the form of a familiar diagram pre-sented in Figure 3.1. Another was his well-known “arbitrage” relation-ship between a “real” asset return (an interest rate j or a profit rate r) anda nominal return i as mediated by the inflation rate ¾,

j = i − ¾.

Ex ante, ¾ has to be interpreted as an expected inflation; ex post, the ob-served rate is often plugged into the equation.

Fisher’s argument in support of this proposition does indeed rest onarbitrage, in a form that will become familiar in later chapters. In dis-crete time, assume that the price of some asset with a real return j is ex-

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pected to increase at the rate ¾ = (Pt+1 − Pt)/Pt. If (short-term) bonds areto be held as an alternative to the asset in question, their nominal return ihas to satisfy the condition

1 + i = (1 +j)(1 +¾).

Expanding the right-hand side gives the Fisher relationship when theproduct j¾ is “small.”

Fisher arbitrage is not supported by the data (Summers 1983;Henwood 1998). As argued in Chapter 4, it is dynamically inconsis-tent with Keynesian liquidity preference theories of the rate of interest.Nonetheless, the real rate/nominal rate distinction is central to mucheconomic discourse. Good analytical (as opposed to weak empirical)support is why it holds its own as an intellectual center of gravity.

Turning to Fisher’s real interest rate theory (a theory of j), Figure 3.1 isthe basic diagram for an isolated individual (“Robinson Crusoe,” in theeconomists’ drastic misreading of that personage’s vivid social interac-tions with his capitalist cronies, enemies, and slaves). It illustrates thetrade-offs between income flows “today” and “tomorrow.”

The “Opportunity” curve concave to the origin is a production-possi-bility relationship, showing how much of today’s income has to be sacri-ficed to generate more tomorrow. Convex to the origin is a “Willing-ness” curve. Its absolute slope is assumed be less than −1 when it crosses

money, interest, and inflation 91

Incometomorrow

y

Constantincome stream

Income todayx

Willingness

45°

Opportunity

Figure 3.1The Fisher diagram.

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the “constant income stream” line with a slope of 45 degrees (or +1).This condition ensures “positive time preference” from Böhm-Bawerk’sfirst two reasons. The implication is that the point of tangency betweenthe willingness and opportunity lines lies below the 45-degree line. The(absolute) slope of the line through the tangency is 1 + j, where j > 0 isthe equilibrium real interest rate.4

The next step is to allow market transactions. The key observation isthat an economic actor will take advantages of opportunities with re-turns exceeding the current interest rate j. In Figure 3.2, for example,someone beginning at point A can “invest” α with a “return” β to get topoint B. She or he can then borrow the sum α + γ to arrive at an equilib-rium C (with the slope of the “interest rate” schedule determining therelative positions of B and C).

An analogous picture can be drawn for someone who lends. Presum-ably, there are people elsewhere in the system who are in fact willing tolend to offset our individual’s net borrowing γ—there is a market forloanable funds. Also, it is usually inadmissible to borrow more than onesaves indefinitely. As will be seen, this “no Ponzi game” condition comesinto its own in models in which time lasts longer than just tomorrow.5

To summarize, the real interest rate in Fisher’s world equilibrates themarket for loanable funds. The nominal rate adjusts to the real ratewhen there is inflation. As Keynes later emphasized, how markets forstocks of financial assets are to be cleared is left unexplained; this weak-

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A

C

B

Income today

Interest rateIncome

tomorrow

β

α γ

Figure 3.2Transactions in theFisher diagram.

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ness led him to develop his own monetary theory of the rate of interest.Like Keynes’s approach, a strength of Fisher’s model is that it can han-dle financial transactions among a multiplicity of agents—as discussedin Chapter 6, it underlies the Modigliani-Miller theorem in a world pop-ulated by well-informed, optimizing financial actors. Such diversity islacking in other contemporary formulations based on “representative”firms and households. Frank Ramsey’s (1928) optimal saving model isthe prototypical example.6 The standard update of Ramsey, usually attri-buted to Cass (1965) and Koopmans (1965), is the topic of the followingtwo sections.

5. The Ramsey Model

Following Abel and Blanchard (1983), we can start by working sepa-rately with resource allocation decisions over time by firms and house-holds, although the institutional distinction between these two sorts of“agents” will prove to be slight. Subsequently, their optimal time pathswill be combined to solve the “social” dynamic allocation problem. Wemeasure all variables relative to the supply of labor L, which for the mo-ment is assumed not to grow (that steady-state growth is a minor exten-sion of the stationary state is illustrated in the following section). Thecapital/labor ratio is k = K/L, consumption per household is c = C/L, ωis the real wage, and g = I/K is the growth rate of capital (ignoring de-preciation as usual). To finance investment, firms issue bonds Z with ashort-term real interest rate j, and z = Z/K.

Both firms and households are assumed to share perfect foresightabout an infinite future—the incredibility of this hypothesis will be la-mented from time to time. If they can foretell all that lies ahead, firmsmight plausibly be supposed to maximize the present discounted value Vof their real cash flow (output less investment and wages) per capita,

V = ρ0

∫ [f(k) − gk − ω]dt = ρ0

∫ Jdt, (3)

subject to the restriction

| = gk. (4)

In (3), f(k) is a neoclassical production function in which output percapita is determined by the capital stock per capita, presupposing Say’smodern law. The “extensive” form of the production function, X =F(K, L), is assumed to have constant returns to scale so that X/L =F(K/L, 1) = f(k). The discount factor ρ is based on the changing bond in-

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terest rate over future time, ρ(t)= exp[−0tj(t)dt], where exp(..) is the ex-

ponential function. Since firms issue bonds to pay for investment, wehave ‰/L = gk. Bond purchases and interest payments show up below inthe household budget constraint (11).

The contemporary standard version of the calculus of variations tech-niques that Ramsey imported into economics from mathematical physicsis known as optimal control theory. The solution procedure starts out byintroducing a “costate variable” or undetermined function of time µ toadjoin the differential equation constraint (4) to the performance func-tion being integrated in (3) to get a “Hamiltonian” expression H = ρJ +µ|. When there is a discount factor like ρ in the maximand, it is conve-nient to work with a costate written as µ = ρq to generate a “present-value” Hamiltonian of the form

H = ρ(J + q|) = ρ[f(k) + (q − 1)gk − ω].

The Hamiltonian is a function of time, in the present problem runningfrom t = 0 to t = ∞. In line with the discussion in Chapter 1, q(t) as itemerges from H will turn out to be the asset price of capital at time t.

The partial derivatives of H with respect to the “state” (or stock) vari-able k and “control” (or flow) variable g can be used to set up “Eulerequations” defining the firm’s optimal investment path. Dynamics of thecostate variable follow from the partial of H with respect to k:

d(ρq)/dt = −∂H/∂k = −ρ[f′(k) + (q − 1)g], (5)

where f′(k) is the marginal product of capital, df/dk. If this equation isinterpreted as running forward in time (perhaps not the most sensibleprocedure, as discussed later), then the discounted capital asset price ρqdeclines more rapidly as the marginal product is higher.

The accumulation equation “dual” to (5) is just (4) once again:

dk/dt = ∂H/∂(ρq) = gk.

In principle, (4) and (5) solve the firm’s dynamic planning problem.Both formulas depend on the capital stock growth rate g, which accord-ing to the optimal control recipe should be determined by one last Eulercondition: ∂H/∂g = 0. But here a small mathematical spanner falls intothe works: the Hamiltonian H is linear in g. There is no simple way tosolve this marginal condition.

More sophisticated evasions exist, but mainstream aggregate growththeory gets around this difficulty in straightforward fashion. It intro-duces “installation” or “shut-down” costs |h(g) = gkh(g) associatedwith capital formation or decumulation. So long as h(g) is conveniently

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nonlinear,7 its presence in the Hamiltonian permits an interior solutionfor g. This revision of Ramsey’s original model, first popularized byEisner and Strotz (1963), may make empirical sense, but it should be rec-ognized for what it is: a mathematical trick designed to ensure smoothaccumulation dynamics over time.

Cash flow including investment costs is J = f(k) − gk(1 + hg) − ω.From an appropriately modified Hamiltonian, the condition ∂H/∂g = 0becomes

q = 1 + h(g) + gh′(g). (6)

With the properties of the function h(g) listed in note 7, (6) makes q = 1when g = 0. By an arbitrary choice of functional form, the capital assetprice is set to its benchmark value of unity when the economy is in asteady state with | = 0.

The evolution of q itself is determined by plugging (6) into (5) as re-written to take into account the presence of h(g). Making use of the factthat ¿ = −j, the differential equation for q becomes

É = jq − [f′(k) + g2h′(g)]. (7)

Equations (4), (6), and (7) describe the behavior of the optimizing firm,based on joint determination of k and q over time.

Postponing consideration of the dynamics of this system until Chapter4, assume for the moment that the economy always has been and everwill be at a stationary state with | = É = 0. Combining (6) and (7) thengives

q = f′(k)/j = 1. (8)

The capital asset price is the marginal product of capital f′(k) capitalizedover an infinite horizon at the (constant) market interest rate j. In long-run equilibrium the marginal product equals the interest rate, f′(k) = j,so that q = 1.

This condition is an application of the q-theory of investment de-mand proposed by Tobin (1969). To explore the causal structure of theRamsey model, it is helpful to consider a linearized version of (8), settingr = f′ so that the profit rate is equal to the marginal product of capital.Noting that (6) makes g an increasing function of q, we get an invest-ment demand function of the form

gi = g0 + αr − θj, (9)

where perturbation terms from linearization of q = r/j fit into g0.Investment rises with the profit rate and falls with the bond interest

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rate. Keynes would not be greatly surprised. Where he and Minskywould differ from the modern interpretations of Ramsey (as discussed inChapters 4 and 8) is with regard to the simple-mindedness of believingthat firms can even pretend to solve an infinite horizon optimizing prob-lem of the sort we are discussing here.

Next we turn to the immortal, identical households making up the cit-izenry. They choose consumption paths by maximizing lifetime utility,

U = exp0

∫ (−Àt)u(c)dt, (10)

subject to the intertemporal budget relationship

Œ = (ω − c)/k + z(j − g), (11)

where u(c) is a “felicity” (or instantaneous utility) function, À is a subjec-tive discount factor, and the term z(j − g) takes into account interest pay-ments to households from firms on their outstanding debt and the “scal-ing” effect of capital stock growth g on the ratio variable z = Z/K.

Details about the Hamiltonian dynamics of a problem similar to (10)and (11) are presented in the following section, as well as in Abel andBlanchard (1983), Blanchard and Fischer (1989), Romer (2001), andmany other sources. If the household felicity takes the frequently postu-lated form u(c) = c1−η/(1 − η) (discussed in more detail below) then inte-gration over time of a household behavioral equation of the form (19) or(20) derived below followed by substitution of the integral of the house-hold income-expenditure balance gives a per capita consumption func-tion

c C L j qk j j j X L= = + =/ ( )[ ( / )] [ ( )/ ]( / )β ω β (12)

with C as total consumption. After the second equals sign, c is propor-tional to total wealth comprising the value of capital per head qk andcapitalized wage income w/j. The proportionality factor b/(j) depends onthe interest rate. The last expression follows when one notes that q r j= /at the steady state. For (12) to make sense economically, the conditionβ( )/j j <1is required. From equation (8) for q, c will depend positively onthe marginal product of capital or profit rate. Depending on the balanceof income, substitution, and wealth effects, dc/dj can take either sign butit is conventionally assumed to be negative.

Dividing k through (12) gives expressions for the capital stock growthrate permitted by available saving,

g u C K j j u s j us = − = − =( / ) [ ( )/ ] ( )1 β (13)

with s j( )<1and ∂ ∂s j/ > 0.

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The full employment assumption that we have been making all alongsets u = Ä, where Ä is constant. Marginal productivity conditions fix theprofit rate r and profit share π = r/u. From (9) and (13) the standardmacroeconomic balance condition gi − gs = 0 for the Ramsey modellinearized around its stationary state comes out as

g0 + απÄ − θj − s(j)Ä = 0, (14)

with the real interest rate j as the implicit adjusting variable.As will be seen in the following section, the full solution to the Ramsey

model is dynamically unstable, because its asset price equations (7) or(18) below incorporate positive feedback. If we ignore this aspect for themoment, then (14) boils down to a relationship in which the real interestrate could vary to bring saving and investment into equality with full em-ployment. The market involved is the one for bonds issued by firms, orloanable funds. A few pages of clunky mathematics and we are steeringright back toward John Stuart Mill.

6. Dynamics on a Flying Trapeze

Now we take up the unstable dynamics, which call for a few special as-sumptions to make the loanable funds story go through. Along withmany other authors, Abel and Blanchard (1983) show that the separateoptimizations of firms and households are equivalent to a single plan-ner’s problem of maximizing household utility

U = exp0

∫ (−Àt)u(c)dt

subject to two restrictions,

c + gk[1 + h(g)] − f(k) = 0

and

| = gk.

As usual in neoclassical CRS models, this “command economy” opti-mizing problem can be implemented by decentralized “agents,” pro-vided that they keep their accounting straight and faithfully carry outtheir assigned maximization tasks. This equivalence between planningand the market is often credited to the cleverness of the invisible hand inguiding optimal growth. In the present context, competitive forces aresupposed to lead the interest rate (or the structure of present and futureshort-term rates, if the economy is out of the stationary state) to adjust inthe market for loanable funds to ensure that saving is equal to invest-

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ment at full employment. Investing firms are differentiated from savinghouseholds only by capital stock installation or shut-down costs, a palereflection of the institutional structure of capitalism that Keynes andKalecki emphasized.

For looking at dynamics, an immediate simplification is to suppressthe minor distinction between households and enterprises altogether(also getting rid of capital stock installation and shut-down costs), sothat household saving is directly channeled into capital formation with-out intermediation through enterprises obtaining loanable funds. On theother hand, to explicate technical debates in the mainstream it is conve-nient to introduce labor force growth at a constant rate n: L(t) = exp(nt)with L(0) normalized to one. It is also customary to weight felicity in theutility integral by the population in existence at any point in time, that is,the payoff function takes the “Benthamite” form exp(−Àt)L(t)u[c(t)].After substitution for L(t), “society’s” planning problem boils down to

max U = exp0

∫ [−(À − n)t]u(c)dt (15)

subject to

| = f(k) − c − nk, (16)

where the final term in (16) reflects the fact that ongoing populationgrowth cuts into the existing level of capital per head. As before, it isconvenient to assume that felicity u(c) takes the constant elasticity form,c1−η/(1 − η), with u(c) = log c for η = 1.8 The elasticity of substitutionbetween values of c at two points in time can be shown to be 1/η. Thelower the value of η, the more slowly marginal utility falls as consump-tion rises. That is, a household with a low η is willing to let its consump-tion levels swing substantially over time.

The maximand in (15) now incorporates a constant (net) discount rateλ = À − n, which will have to be positive for a solution to (15) and (16)to exist (without the condition λ > 0, the utility integral (15) will be un-bounded). An equivalent statement based on results to be developed im-mediately below is that a long-run real interest rate À smaller than thesteady-state output growth rate n is not consistent with a dynamic equi-librium. As discussed in Chapter 6, the À > n condition doesn’t make alot of sense outside a dynamic optimization framework, because it ishard for a borrower to make ends meet in the long run when the rulinginterest rate exceeds the growth rate of real income. But for now weleave that complication aside.

Proceeding as with the firm’s investment problem discussed above,

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we can work with a costate variable written as exp(−λt)ξ, with ξ as soci-ety’s capital asset price analogous to the firm’s q. The present valueHamiltonian becomes

H = exp(−λt)u(c) + ξ[f(k) − c − nk].

The Euler conditions for a locally optimal growth path are

u′ = du/dc = ξ, (17)

and

−Õ = f′ − À. (18)

Hat calculus shows that the growth rate of u′ is û′ = −ηÒ, in turnequal to ξ from (17). Substituting into (18) gives a condition known asthe “Ramsey-Keynes rule,”9

ηÒ + À = f′. (19)

This equation could just as well be called the Böhm-Bawerk rule, be-cause it combines his three reasons for a positive interest rate. The ηÒterm reflects how changing “circumstances of want and provision” ascaptured by Ò affect saving choices, while À captures “underestimation ofthe future.” The profit rate f′ summarizes investment possibilities, forthe third reason. The rule basically says that an interest rate (or “socialrate of discount”) on the left of the equals sign has to be set equal to aprofit rate on the right to arrive at an accumulation optimum. At steadystate with Ò = 0 and ú = n, the rule boils down to f′ = À or rate of profit= rate of time preference = steady-state rate of interest.

As is often the case with neoclassical macroeconomics, these resultslook very neat; only their underlying hypotheses and verisimilitude areopen to question. In particular, the intertemporal behavior of dynamicmodels like the present one can seem implausible. The details are whatwe take up next.

Equation (16) restated for convenience and a rearranged version of(19) form a coupled dynamic system:

| = f(k) − c − nk (16)

and

˜ = (c/η)(f′ − À). (20)

The two equations clearly allow for a steady state at which ˜ = | = 0. Toinvestigate the dynamic behavior of c and k in the vicinity of this point,we can form the 2 × 2 Jacobian matrix of first partial derivatives of the

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right-hand side of the equations, and plug in steady-state values of k andc. The matrix takes the form

Mf nc f

=′− −

10( / )η

(21)

in which f″ = d2f/dk2 < 0.The necessary condition for local stability of the system (16)–(20) is

that both eigenvalues of M should be negative at the steady state. Be-cause the trace of a matrix is the sum of its eigenvalues and the determi-nant is their product, we need Tr M < 0 and Det M > 0 for stability.10

The determinant condition is violated in (21). With regard to the trace,we have already observed that f′ = À at the steady state. Because the con-dition À > n is required for a solution of (15) and (16) to exist, Tr M ispositive. The steady-state solution is dynamically unstable. There is onepositive and one negative eigenvalue (Det M < 0), and the positive roothas greater absolute magnitude (Tr M > 0).

Figure 3.3 is a “phase diagram” which attempts to illustrate what isgoing on. Let k* be the solution of the equation f′(k) = À. Then from(20), ˜ = 0 when k = k*, as illustrated by the vertical line. For values ofk less than k*, ˜ > 0 and the reverse is true for k > k* (as indicated bythe small arrows). The locus of points along which k is stationary or | =

100 chapter three

A

S

S

Consumptionper capita

c

Capitalper capita

k

k* kG

c = 0.

k = 0.

Figure 3.3Saddlepath dynamicsin the Ramseymodel.

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0 is hump-shaped, taking on a negative slope for high values of k as cap-ital’s “marginal product” drops off due to decreasing returns to a singlefactor.11 From (16), the capital/labor ratio rises for points below thehump and falls for those above it.

The steady state with ˜ = | = 0 is at point A. However, as the curvedarrows illustrate, the equilibrium is a saddlepoint. Only trajectories be-ginning along the “saddlepath” SS will reach the steady state.12 All oth-ers bend toward and then away from SS in the fashion of the “turnpike”dynamics beloved by mainstream theorists in the 1960s. An immediateconclusion might be that describing macroeconomic dynamics with anequation pair like (16) and (20) is not a reasonable strategy to pursue.

The current generation of mainstream economists, however, prefer totreat (16) and (20) as an accurate description of how agents behave. Notbeing satisfied with the saddlepath as a referential turnpike, they wantthe economy always to be on it (or even better, always at steady state). Ifsuch a short-run equilibrium is perturbed, the “jump” or control vari-able c will immediately adjust to put the system back on the straight andnarrow.

An example appears in Figure 3.4, in which the | = 0 locus moves up-ward because of a technical advance, so that point B is the new steadystate and the old steady state, point A, becomes an initial position. An“ordinary” trajectory beginning at A would head southeast toward thehorizontal axis and zero consumption, like many an old sailing ship withluckless navigation in the “roaring forties” south of Cape Horn. An in-stant jump of consumption from point A to point B can prevent this ca-tastrophe. Under full rationality, the argument goes, this unique eventwill occur.

Put a bit more formally, fully competent agents would avoid thePonzi-like strategy of running down the capital stock to support risingconsumption, as finally happens along trajectories to the left of SS in Fig-ure 3.3. Such behavior will not be observed. Trajectories to the rightof SS all lead the ratio of households’ discounted consumption to dis-counted income to go to zero as they engage in overinvestment (Romer2001). They can surely do better by sticking to the saddlepath. For theimmortal, omniscient Beings solving (15) and (16), adding such a “trans-versality condition” to their local optimizing rule (20) may not be toomuch to ask; all they have to do in a multisectoral version of the model issteer the economy within a set of measure zero in a high-dimensionalphase space.

Four final points. The first is that a planning problem with dynamicslike (16) and (20) but with a finite horizon T instead of ∞ in the integralin (15) sidesteps some of the metaphysical trappings of the standard

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Ramsey model, and moreover is easy to solve. It is a “two-point bound-ary value” problem with an initial value k(0) of the state variable and“reasonable” final values for c(T) and k(T), which emerge from solving(16) and (20) with ˜ = | = 0.

Substituting c(T) into (17) gives a final value ξ(T) for the costate vari-able. A revised version of (18),

Ó = −ξ(f′ − À), (18′)

can be solved backward in time from the terminal value ξ(T). Backwardintegration of this differential equation for ξ is stable, and from (17)gives values of c over time as well. Plugging these into (16) integratedforward in time from k(0) amounts to a feedback decision rule for thestate variable. Iterating on (16) and (18′) in this fashion easily solvesthe planning problem from a “plausible” initial reference path (Brysonand Ho 1969; Kendrick and Taylor 1970), and for T = 100 or 10,000years the results will not differ noticeably from the infinite horizonproblem.

The question that arises is why such a planner’s problem (which mightbe an interesting reference path for policy discussion) is taken by themainstream as an exact description of how decentralized agents behave

102 chapter three

A

B

Consumptionper capita

c

Capitalper capita

k

c = 0.

k = 0.

Figure 3.4Effects of a produc-tivity increase in theRamsey model.

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as T goes to infinity. For the reasons discussed above, many people findsuch a notion strange. Moreover, as discussed in Chapter 6, even theplanner’s problem becomes computationally infeasible once uncertaintyis brought into the equations. That is perhaps the fundamental difficultyfor economists willing to take the Ramsey model as descriptive of indi-vidual behavior on its own terms. Even armed with supercomputers,“agents” could not comply with their assigned behavioral model.

The second observation is that in Figure 3.3 the equilibrium capital/la-bor ratio k* is less than the “golden rule” ratio kG at which steady-stateconsumption per head is maximized (by setting f′ = n in (16) with | =0). In contrast to Pasinetti’s model discussed in Chapter 2, the profit rateexceeds the growth rate because k* < kG. A Ramsey steady-state equilib-rium is not a “natural system.”13

Third, full employment dynamic adjustment in Ramsey models basi-cally relies on supportive changes in the whole structure of interest ratesover time. An example in the present case is given by a reduction in thediscount rate À. In Figure 3.3, k* would shift to the right, dragging thesaddlepath with it. Consumption c would jump down from point A tothe dislocated SS schedule, and then increase back along it to the newequilibrium on the “| = 0” locus. Because −ηÒ = Õ = À − f′, asset pricesand thereby interest rates would adjust to accommodate this movementover infinite time (for more details about the asset price/interest rate link-age, see Chapter 4).

What happens if the term structure of interest rates is not fully flexible,because of slowly changing expectations and large bond reserves heldby speculators? Then the Say’s Law assumption underlying the Ramseymodel becomes difficult to sustain. Excess aggregate demand is morelikely to be driven toward zero by changes in the level of economic activ-ity than by price-driven movements in investment and savings schedules.This argument, made in a classic paper by Kaldor (1960a), goes unan-swered in optimal savings exercises, in which perfect foresight super-sedes the workings of real world financial markets.

Finally, introducing artifacts like money (typically entering into theutility function) and slow price adjustment to a discrepancy between ag-gregate demand and aggregate supply can permit transient unemploy-ment in Ramsey-style models—Ono (1994) neatly works through onesuch exercise. Hahn and Solow (1995) engage in similar maneuvers forthe overlapping generations model we take up next. These more“Keynesian” approaches, however, do not alter the basic causal struc-ture of the models—they just resemble a shift from a system like the onein Figure 2.2 of last chapter to Figure 2.3.

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7. The Overlapping Generations Growth Model

As the foregoing discussion suggests, over the last decades of the twen-tieth century mainstream macroeconomists devoted a good deal of ef-fort to generating MIRA foundations for capital accumulation. BesidesRamsey and Tobin q exercises, the other major thrust went toward con-struction of overlapping generations (OLG) models in which “young”and “old” agents cohabit the same economy.

Because we have just worked through a Ramsey formulation, it makessense at this point to set up a simple discrete-time OLG model to drawcontrasts and also point out instability and inefficiency problems. Withaging populations in industrial economies, the OLG story has influencedthe pension policy debate. The section closes with an OLG-based analy-sis of social security systems, to be compared with a more Keynesian dis-cussion developed in Chapter 5.

The story in the canonical Diamond (1965) version of the model isthat each “agent” lives two periods, working in period t and subsistingon accumulated saving before s/he (it?) dies at the end of period t + 1.Faced with such a life history, an agent optimizes two-period consump-tion. A common statement of the choice problem is to maximize a non-Benthamite (felicity unweighted by population size), discrete-time ver-sion of the utility integral (15) of the Ramsey model,

U = [(ct)1−η/(1 − η)] + [(ct+1)1−η/(1 − η)]/(1 + À)

subject to the intertemporal budget constraint

ct + ct+1/(1 + rt+1) = ωt, (22)

where the subscripts denote time periods. Future consumption is dis-counted at “next” period’s profit rate rt+1, so that agents require perfectforesight only over their own lifetimes. Their saving automatically takesthe form of physical capital accumulation because of Say’s Law. The in-come available for saving and first-period consumption comes from thereal wage ωt; second-period consumption is paid for by first-period sav-ing and accumulated profit income.

After routine grinding,14 saving per person at time t (that is, ωt − ct) isgiven by the expression

( )

( ) ( )(

(

( )/ /

1

1 11

1

11 1

+

+ + +

=

+−

+−

r

rst

tt

η η

η η ηω

)/

Àrt t+1 ) .ω

The algebra is intimidating, but simplifies nicely. When η = 1 (theCobb-Douglas case of logarithmic utilities),

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s(rt+1) = 1/(2 + À). (23)

For values of η “close” to one, changes in the s(rt+1) term in responseto movements in the profit rate will not be important and in the follow-ing discussion are ignored. We assume s(rt+1) = s, a constant.

The parameter s stands for saving per person, so that total saving issωtLt = sωtbtXt (with bt being the labor/output ratio and Xt output). Thecapital stock growth equation is

Kt+1 = Kt + sωtbtXt

or

(Kt+1 − Kt)/Kt = gt = s(ut − rt) (24)

(with ut = Xt/Kt), after substitution from the accounting identity ut =ωtbtut + rt. The direct effect of a higher profit rate rt is to reduce gt in (24).From Chapter 2’s wage-profit frontier ωt and rt vary inversely, while sav-ing and growth rise with wage income. The resulting “perverse” re-sponse of accumulation to profitability can produce dynamic instability,as we now demonstrate.15

The state variable of interest is kt = Kt/Lt, with assumed full employ-ment of labor and population growth at rate n: Lt+1 = (1 + n)Lt. Drop-ping subscripts for the moment, one can use hat calculus tricks to get thefollowing differential change relationships from neoclassical productiontheory:

du = −(1 − π)(u/k)dk and dr = (r/σu)du,

where π is the share of profits in output and σ is the elasticity of substitu-tion between capital and labor. Plugging these results into (24) minussubscripts and using the identity r = πu shows that

dg = −suk

( )σ π

σ

−(1 − π)dk. (25)

The sign of dg/dk depends on the term σ − π, with implications to be dis-cussed presently.

The next step is to set up a growth equation for kt. Using the relation-ships Kt+1 = (1 + gt)Kt and Lt+1 = (1 + n)Lt, it comes out as

kt+1 =11

11

+

+=

+ −

+

gn

ks u r

nk

tt

t tt

( ). (26)

In discrete time, the local stability condition for this nonlinear differ-ence equation is that the absolute value of dkt+1/dkt has to be less thanone. With its dynamic responses thus limited, an equation like (26) be-

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comes a “contraction mapping” converging to a stationary solution kt+1

= kt = k*. Stable dynamics are shown in the upper diagram of Figure3.5, with the “accumulation” line showing kt+1 as a function of kt. Thereis convergence from an initial capital/labor ratio k0 to k*. The lower pic-ture illustrates the unstable case.

106 chapter three

45°

Accumulation

Accumulation

Capital/laborratiokt+1

Capital/laborratiokt+1

45°

Capital/laborratio

kt

Capital/laborratio

kt

k0

k0

k*

Figure 3.5Stable and unstabledynamics in a sav-ing-driven OLGmodel.

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Combining (25) with subscripts restored and (26) shows that the rele-vant differential expression is

dkt+1 =1

11 1

++ −

−−

ng su dkt t

tt t[( ) ( )( )] .

σ π

σπ (27)

At an initial steady state, gt = n. Then dkt+1/dkt will be less than one andthe OLG growth process will be stable so long as the term after the mi-nus sign in the brackets in (27) is positive, that is, σ > πt.

The narrative is that the profit rate responds more strongly to changesin ut when σ is small. There is a constant profit share when σ equals onein the Cobb-Douglas (production function) special case. For values of σnear zero, on the other hand, redistribution toward the elderly becomesimportant in the macro adjustment process. When kt decreases or thelabor/capital ratio increases, the increased labor input makes the out-put/capital ratio ut go up as well. The higher ut leads to a big increase in rt

when σ is small. But the elderly agents who receive profit income justspend it to consume. As a consequence, overall saving and the growthrate gt decline, kt+1 falls further, and the economy diverges from steadystate. With savings-driven accumulation, macro adjustment via incomeredistribution breaks down, if the beneficiary group has a high propen-sity to consume. In American terms, let Generation X beware!16

Rather than potential instability in OLG models, the mainstream hasfocused on another problem—their potential inefficiency because theequilibrium capital/labor ratio k* can exceed the golden rule value kG. Ifthat is the case, the profit rate (or marginal product of capital) r will bebelow the population growth rate n because capital is very plentiful.From the hump-shaped relationship in Figure 3.3 (which broadly appliesin an OLG world as well), consumption per head is maximized when k= kG. Hence for k > kG, consumption could be increased by cutting backon the capital stock. This is the inefficiency.

This problem does not arise in Ramsey models because growth trajec-tories to the right of the separatrix SS in Figure 3.3 are ruled out by atransversality condition. Immortal, omniscient actors won’t get them-selves on such a path. However, coordination problems across genera-tions could push an OLG economy into Pareto inefficiency.17 Becausesaving comes from real wages, which are high when the profit rate is low,one signal could be a small saving rate. Look at equations (26). At asteady state, kt = kt+1 and gt = n. If we drop subscripts, the relationshipreduces to n = s(u − r), or

r = u − (n/s). (28)

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It is easy to see from (28) that r < n when u < n(s + 1)/s. For u = 0.3(observed values for the GDP/capital ratio rarely go outside the range0.2–0.4) and n = 0.01, s < 0.035 would give inefficiency. It doesn’t haveto happen, but s in such a range is possible—consider American house-hold or even private saving rates as discussed in Chapter 1.18

An alternative is to test directly whether the profit rate lies below thegrowth rate. More generally, under “risk” in the sense that completeprobability distributions can be put on future events (an epistemologicalposition which Keynes deemed absurd, as we will see), Abel, Mankiw,Summers, and Zeckhauser (1989) show that the appropriate test for ef-ficiency is that the profit share of GDP should exceed the investmentshare—capital income contributes to consumption when it exceeds so-cial accumulation needs. Seven industrialized economies turn out to passthis test. For economists intrigued by academic debates, such resultsmay be comforting. Much more fundamental is the fact that while over-all profit income may exceed investment, it is also true that in industrial-ized capitalist economies corporations distribute a substantial portion oftheir profits to households. In turn, households’ acquisition of new busi-ness liabilities may represent an important supplement to retained earn-ings in funding capital formation. All the financial churning that standsout in Tables 1.4 and 1.5 is simply ignored in the OLG (in)efficiency dis-cussion. Are those big financial flows completely a veil?

For future reference, both Marxist and “Austrian” business cyclemodels (the latter originating from the London School of Economics inthe 1930s) invoke “excessive” investment in the recent past as a fun-damental cause of cyclical downswings. There is certainly a family re-semblance to inefficiency in the OLG framework. For more details, seeChapter 9.

Despite its peculiar assumptions about saving, the OLG model hasemerged as the principal theoretical vehicle for the analysis of pensionand social security systems. The standard approach is based on modi-fications to the household budget restriction (22). The general idea isthat households are taxed (in lump-sum fashion) an amount q in the firsthalf of their lives and receive a lump-sum transfer z in their second pe-riod. Under such a scheme (22) has to be rewritten as

ct + ct+1/(1 + rt+1) = ωt − q − [z/(1+rt+1)]. (22SS)

Most existing pension schemes can be modeled as a blend of two ex-treme forms:

“Fully funded” plans simply take the payroll deduction q and invest itat the going return rt+1 so that z = (1 + rt+1)q. The budget constraint un-

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der social security, (22SS), reduces to (22) and the foregoing analysis isunchanged.

“Pay-as-you-go” (or “pay-go”) schemes sum up all young households’payments of q and transfer them to the less numerous older cohort. Eachsuch household thereby receives z = (1 + n)q. In (22SS) the last term tothe right doesn’t vanish, and there will be effects on the accumulationequation (26). It is easy to see that if rt+1 > n, the term in brackets in(22SS) will be positive, reducing wealth and presumably inducing house-holds to save less. Even in the opposite “inefficient” case, one can show(Blanchard and Fischer 1989 for the details in the Cobb-Douglas utilitycase) that the increase in saving from greater wealth due to the pensionscheme will be less than the saving loss due to the tax q. Hence overallsaving will decline in general.

In the upper diagram of Figure 3.5, the effect will be to shift the Accu-mulation locus downward. The economy will converge to a steady statewith a lower capital/labor ratio k*, implying lower wealth per capita, alower steady-state real wage, and a higher rate of profit. The U.S. socialsecurity program is close to being pay-go. Results of the sort just de-scribed are prominent in the propaganda of people who want to changethe system. In their view, Roosevelt’s creation creates an unconscionablereduction in social saving.

8. Wicksell’s Cumulative Process Inflation Model

A soupçon of Irving Fisher aside, the foregoing real interest rate modelsdo not figure in The General Theory. The circle of economists in whichKeynes moved was much more focused on the distinction between natu-ral and market rates of interest. The macroeconomic background in thedecades on both sides of the year 1900 involved business cycles in whichprice fluctuations up and down were relatively more significant than out-put changes, with the shift toward production adjustments only comingwith the 1920s and 1930s (Nell 1992; Sylos-Labini 1993).19 Price adjust-ments due to the market and natural rates getting out of gear were a nat-ural analytical construct. The market rate(s) could be observed, whilethe unobservable natural rate was believed to emerge from marginalconditions of the sort developed in the Ramsey model or, better, from aFisherian market in which all participants are solving their own privateutility maximization programs while engaging in financial transactionswith one another.

Macroeconomic debate centered around this perspective. As Amadeo(1989) argues, a post-Wicksellian macroeconomic model certainly didexist. It was a blend of credit-driven endogenous money creation as

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described by Wicksell (1935) and Schumpeter (1934), and the inflationtax and forced saving as macro adjustment mechanisms analyzed bySchumpeter, Robertson (1933),20 and Keynes (1930). Effective demandwas implicit, despite a general acceptance of Say’s Law (perhaps an ade-quate rough-and-ready description of the relatively minor output fluc-tuations over the cycle). The full employment, zero inflation natural ratewas a “center of gravitation” for the system, but played little role in itsday-to-day operation.

What did matter in Wicksell’s own cumulative process model—the in-tellectual prelude to The General Theory—were interactions betweenthe inflation tax and the interest rate charged by banks, as mediated bya saving-investment process. The accounting appears in the SAM ofTable 3.2. (Until the following section, ignore the entries in column 7and cell B4.)

The financial side of the economy is treated as a pure credit bankingsystem—the only financial claims are those associated with banks. Theirconsolidated balance sheet is Af + Ag = D + M, where Af and Ag standfor advances (credits, loans) from the banks to firms and the governmentrespectively. “Desired” deposits from households are D, and M is an en-dogenously adjusting money (or currency) supply. Column (6) in theSAM restates the banks’ balance sheet in flow terms (where a “dot”above a variable as usual denotes its time derivative).

The driving force in this system is the evolution of total bank credit A= Af + Ag, which rises with capital formation and government spending.

110 chapter three

Table 3.2 A SAM incorporating the inflation tax (all variables scaled by the value of capital stock).

Current expenditures

Change inbanks’ claims

Change ingovernment

bonds TotalsOutputcosts

House-holds Firms Government Investment

(1) (2) (3) (4) (5) (6) (7) (8)

(A) Output uses γh γg g uIncomes(B) Households (1 − π)u jB/K ξh

(C) Firms πu ξf

(D) Government 0Flows of funds(E) Household

“noninflationary”σh − &/D PK − &/B K 0

(F) Seigniorage ( $P + g)/V − & /M PK 0(G) Firms σf −g & /A PKf 0(H) Government (σg) & /A PKg

&/B K 0(I) Totals u ξh ξf 0 0 0 0

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The key variable driven is household saving or (in Robertson’s terminol-ogy) “lacking” induced by faster price increases. The mechanism ap-pears in the “seigniorage” (another term for the inflation tax) row (F).Before exploring the model’s causal structure, we should look at the restof the SAM.

All variables are normalized by the value of the capital stock PK (theonly nonfinancial asset in the system), and u=X/K as usual. Say’s Law ispresumed, so that u is predetermined. Column (1) shows how output issplit between household and enterprise income flows, where π is theprofit share. Because forced saving will not be brought into the presentdiscussion, π will also be predetermined (by marginal productivity con-ditions, for example, if one is so inclined).

Row (A) shows that on the demand side, u is appropriated by house-hold consumption γh, government consumption γg, and investmentspending g = I/K (all three components of final demand are scaled to thecapital stock). We will shortly specify an investment function, while γg ispresumably set as a policy variable. How, then, is γh going to adjust en-dogenously to satisfy the row (A) accounting balance γh + γg + g = u?

To begin to answer from the blueprints, observe that in the flows offunds row (G) firms fill their financial deficit g − ξf = g − πu by takingnew net credits from the banking system in the amount ®f/PK.21 Govern-ment is assumed to have no income in row (D), but it spends γg in column(4). In row (H), its negative saving (σg) is financed by banks’ advances®g/PK. In the absence of inflation, households in row (E) desire to saveσh, which (because they have no other option) they hold as new bank de-posits ©/PK.

What happens if (®f + ®g)/PK > ©/PK, that is, new loans from thebanking system exceed new deposits? To balance their books, banks willissue currency M in the quantity /PK = (®f + ®g)/PK − ©/PK. In addi-tion to all the foregoing accounting, we assume that the equation of ex-change, MV = PK, applies with a constant value of V (a restriction to berelaxed soon). With Say’s Law in force, it is a matter of convenience touse PK instead of PX on the equation’s right-hand side. Hat calculusshows that þ = ¾ + g, or /PK = (¾ + g)/V.

The last equation is row (F) of the SAM. The interpretation is thathouseholds are hit by the inflation generated by credits created to “fi-nance” demand for commodities by government and firms. These actorshave a prior claim on output, ratified by money creation. Householdsare crowded out of the market, and have to cut back their consumptionas a consequence. To make the accounts work out so that macro balanceγh + γg + g = u will hold, the required reduction is (¾ + g)/V.

How can this particular amount be rationalized? The usual story is

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that the loss in real balances M/P induced by a price increase ¯ is −(M/P)¯. The public is supposed to raise its saving by this amount to re-constitute its wealth when the price level rises—a rational act. Alterna-tively, faster inflation means that people need to hold more money fortransactions purposes; operating with the impoverished asset and liabil-ity structure of column (6) of the SAM, the only way that they can buildup currency holdings is to save more. Similar reasoning applies to thehigher transactions balances needed to deal with growth of the real cap-ital stock at rate g.

The next steps are to consolidate the accounts to get an aggregate de-mand or investment-saving balance, and then to postulate an investmentfunction. Presumably, the latter should depend on the real interest rate j= i − ¾, where the nominal rate i is set by the banking authorities. In-deed, Wicksell’s central argument is that inflation is provoked when theinterest rate in his pure credit banking system is pegged below its “natu-ral” level. To see how, we can consolidate rows and columns in Table 3.2to get the following equation for aggregate demand:

γg + [1 − (1/V)]g(i − ¾) − s(i − ¾)u − (1/V)(¾) = 0, (29)

where su = σh + σf. We assume (with scant empirical justification) thathousehold saving apart from the inflation tax responds positively to thereal interest rate as in the models of previous sections, and that invest-ment demand g is an inverse function of the same variable. Equation (29)says that if the nominal rate i is pegged so that there is incipient excessaggregate demand,

Q(i, ¾) = γg + [1 −(1/V)]g − su > 0, (30)

then ¾ will immediately jump up to squeeze real household expenditurevia the inflation tax to restore macroeconomic balance.22

Is this adjustment stable? To address this question, we must look atthe partial derivatives of Q(i, ¾) in (30). Because g falls and s rises with ahigher interest rate, it is clear that ∂Q/∂i < 0. On the other hand, ∂g/∂¾ ispositive, because a faster inflation rate reduces the real interest rate,thereby cutting saving and stimulating investment demand.23 Although itis built into most models, there is no reason to take the investment link-age seriously, especially in high-inflation economies. The reason is that afaster price spiral adds so much uncertainty to the system that invest-ment plans are almost always cut back. More formally, ¾ itself shouldenter as a separate argument in the investment function, with a negativeimpact. Similarly, the partial derivative ∂s/∂¾ < 0 can be taken with agrain of salt, especially after an inflation process has settled in and non-

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affluent people find that their real spending power has been eroded ac-cordingly.

The upshot is that the effects of ¾ in the function Q(i, ¾) in (30) are ofuncertain magnitude and sign. From (29), overall aggregate demandQ(i, ¾) − (1/V)¾ almost certainly depends negatively on the rate of infla-tion via the inflation tax. Because demand also responds inversely to theinterest rate i, the “Inflation” locus along which (29) is satisfied in Figure3.6 has a negative slope.

To play against this schedule, Wicksell argued that after inflation per-sists for a time, banks (or the Central Banker) will voluntarily raise theinterest rate to limit loan demand and cut down on losses of reserves,say, according to a rule such as

di/dt = θ¾ + φ(i − i*), (31)

where i* is the target or natural nominal interest rate. Usages of theword trace far back in time, but the proximate sources for modern “nat-ural” employment rates or NAIRUs are the Wicksellians. The diagramssketched in Chapter 2 and developed at great length later basically sub-stitute the real wage ω or the labor share ψ for the nominal interest rate ion the vertical axis of Figure 3.6.

Coming back to equation (31), another possibility is that the bankingauthorities might seek to stabilize the real interest rate j = i − ¾,

di/dt = θ′¾ + φ[j* − (i − ¾)].

money, interest, and inflation 113

A B

C

Interest ratei

Inflation rateP

Bank response

Inflation

dtdi 0=

ˆ

Figure 3.6Dynamics of aWicksellian cumula-tive process.

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This equation reduces to (31) with i* = j* and θ = θ′ + φ, so we canconsider either case. If the real rate is targeted, then θ > φ in (31), a con-dition that turns out to be of interest below.

The “Bank response” curve in Figure 3.6 represents the conditiondi/dt = 0 giving a positively sloped relationship between i and ¾. An au-tonomous increase in aggregate demand (say, from higher public spend-ing γg) immediately makes the inflation rate jump upward from A to B.Banks then begin to raise interest rates until a new steady state is reachedat C. Inflation will be forced back closer to its initial level insofar as theBank response schedule is steep, that is, θ >> φ in (31), but for finite pa-rameters ¾ will increase at least somewhat.

The diagram also shows that the nominal interest rate will be higher inthe new steady state, while a bit of manipulation indicates that the realrate will increase when θ > φ. But then investment g will decline, and sowill the steady-state rate of growth. In other words, if banks respond ag-gressively to inflation by raising interest rates (in particular, if they try tostabilize the real rate j by substantially raising the nominal rate i), theymay force investment to be reduced enough to make fiscal dissavingcrowd out growth in the medium run. In Wicksell’s canonical monetar-ist inflation model, there is no automatic transition from inflation stabi-lization to renewed capital formation, a lesson that is too familiar indeveloping economies afflicted with the medications of the InternationalMonetary Fund.

Moreover, persistent inflation means that the desired level i* of the in-terest rate in (31) is not attained. Despite its marginalist anchors, thenominal “natural” rate becomes a moving target, depending on the un-derlying inflationary trend (a result of the interactions of aggregate de-mand with wage indexation and bank responsiveness, in a minimally re-alistic model)—a point perhaps first raised by Myrdal (1939).

As a final exercise, we can elaborate on analysis already sketched inChapter 2 by introducing the monetarists’ preferred stylized fact that ve-locity tends to increase with the inflation rate, say,

V = V0 + v¾. (32)

That is, people “flee money” by reducing their currency and deposit bal-ances as inflation speeds up. Econometric estimates of the parameters V0

and v usually take values between one and ten.Assume, realistically, that the current inflation rate ¾ is accurately ob-

served but that there is uncertainty about its rate of change. If the ex-pected value of d¾/dt is E(d¾/dt) and households adjust their money bal-ances according to this expectation,24 then (32) suggests that the change

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in velocity over time should be written as Î= dV/dt= vE(d¾/dt). Substi-tuting this expression into the growth rate version of the equation of ex-change (interpreted as a dynamic money demand function), þ + Ó = ¾+ g and rearranging gives an expression for E(¾),

E(d¾/dt) = (V/v)(¾ + g − þ).

The natural next step for a modern economist of monetarist or newclassical inclination is to assume rational expectations or (more preciselyin the present context in which we are ignoring random prediction er-rors) myopic perfect foresight with regard to the change in the inflationrate, E(d¾/dt) = d¾/dt. Households correctly estimate d¾/dt, so that theformula above can be restated as a differential equation

d¾ /dt = (V/v)(¾ + g − þ). (33)

Evidently, there is a positive feedback of ¾ into d¾/dt. What are theimplications of such a possibly destabilizing linkage? After substitutionof various relationships from Table 3.2, (33) can be rewritten in the form

d¾/dt = (V/v)[¾ − VQ(i, ¾)], (34)

where Q(i, ¾) is defined in (30). This differential equation replaces thestatic relationship (29), which can be restated as

VQ(i, ¾) − ¾ = 0. (35)

The steady-state solution of (34) at d¾/dt = 0 satisfies (35), but super-ficially the dynamics are richer because (34) is coupled with (31) in atwo-dimensional system. The most realistic case is probably the one inwhich the inflation tax dominates other responses to ¾ in the bracketedterm on the right-hand side of (34) so that d(d¾/dt)/d¾ > 0.25

We are following the recipe spelled out in connection with the Ramseymodel, and to check on stability we have to investigate the properties ofthe two equations’ Jacobian matrix. The sign pattern of the partial deriv-atives turns out to be

$

$P

dP/dtdi /dt

i+ ++ −

The negative determinant signals a saddlepoint, with the two eigen-values having opposite signs. The phase diagram is in Figure 3.7.

From an initial equilibrium at A, the figure shows the adjustment pathwhen the curve along which d¾/dt = 0 shifts rightward to give a newsteady state at C. Inflation jumps from A to B, and then both ¾ and i in-

money, interest, and inflation 115

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crease along the saddlepath SS until they get to the new equilibrium. Thisscenario closely resembles the one in Figure 3.6, with the main differencebeing that the initial jump in inflation is a bit smaller in Figure 3.7.

To summarize, the Wicksellian model presented here presupposesSay’s Law and involves macroeconomic adjustment via interest ratechanges and (more spectacularly) the inflation tax. The inflation rate isthe “jump” variable that permits rapid equilibration of the equation ofexchange in growth rate form. At least short-run perfect foresight aboutd¾/dt or the change in the inflation rate has to be invoked if the economyis to leap to a saddlepath as in Figure 3.7. Such hypotheses always begquestions about the sources of the precise economic knowledge that theyentail, but perhaps the interrogation can be less severe for the Wicksellmodel than for an infinite horizon Ramsey machine.

More important from the perspective of The General Theory is thefoundation of Wicksellian models on injections and leakages as sourcesand sinks of effective demand, along with their recognition of the factthat some variable has to adjust in the short run to ensure macro-economic equilibrium. Compared with Wicksell, one contribution ofKeynes and Kalecki was to recognize that prices are more credibly deter-mined by “slow” dynamics (of the sort already sketched in the struc-turalist inflation models of Chapter 2) than by saddlepath trapeze leaps.Their more important innovation was to drop Say’s Law. In line with the

116 chapter three

C

Interest ratei

dtdi 0=

dtdP

AB

S

S

Bank response

Inflation rateP

0=ˆ

Figure 3.7The cumulative pro-cess with rationalexpectations.

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nature of the twentieth-century business cycle, capacity utilization be-comes the jump variable par excellence.

The final point worth noting and to be developed at length later in thisvolume is that overthrowing Say’s Law turned out to be no trivial task.Both the new classical and new Keynesian models currently at the pro-fession’s center stage bear a much closer relationship to the formulationsof Wicksell and his successors than they do to those of Kalecki andKeynes.26 The main difference is that the stable inflation rest point is nowcalled a NAIRU instead of a natural rate of interest.

9. More on Inflation Taxes

Inflation taxes are hardy perennials in monetarist and new classical gar-dens. Before turning to the Keynesian interpretation of effective demand,it makes sense to peek briefly at three species that have flourished in re-cent years—the inflation tax in public finance, its stability or instabilityin non-Wicksellian contexts, and an exotic new classical orchid calledthe “tight money paradox.”27 The thrust of the argument is that these re-cent models work with an even more limited set of assets than the oneused by Wicksell, and are correspondingly less relevant to realistic policychoice.

In most monetarist discourse, the fact that firms can finance the gapbetween their investment and saving by borrowing from banks is ig-nored—the government gets all the blame for the inflation tax. In mostmodels, the tax is analyzed in terms of monetary “real balances” m =M/P held by households. They evolve over time according to the rela-tionships

/P = þm = ~ + m¾. (36)

In a stationary state, g = ~ = 0. Under such circumstances, inflation taxor seigniorage revenue /P is equal to m¾. It is used to finance the realfiscal deficit ∆.

Under inflationary conditions, the standard mainstream money de-mand function was introduced by Cagan (1956):

m = m0 exp(−α¾). (37)

Setting m0 = 1 gives the following expression for seigniorage:

/P = ¾ exp(−α¾). (38)

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This formula generates the “Laffer curve” for the real proceeds of the in-flation tax sketched in Figure 3.8. It is easy to show that revenue is maxi-mized when ¾ = 1/α at point A.

The next step is to consider the effects of inflation on “ordinary” taxrevenue. If the tax system is not indexed to the inflation rate—an institu-tional shortcoming that is remedied sooner or later in most inflation-prone economies—so that there are lags in the collection process, realtax returns will decline as ¾ goes up.28 This “effect” was emphasized ina Latin American context by Olivera (1967) and Tanzi (1978). Usingtricks like those deployed to analyze conflicting claims inflations inChapter 2, the latter considers a collection lag of n months. If T(¾)stands for real tax revenue when the annual inflation rate is ¾ (in discretetime), he shows that

T(¾) = T(0)/(1 + ¾)n/12. (39)

The declining revenue is illustrated by the “Olivera-Tanzi curve” inFigure 3.8. The inflation rate ¾* that generates maximum fiscal reve-nue is less than 1/α because of the Olivera-Tanzi tax drag. At ¾*, reve-nue from the inflation tax is OB, from other taxes it is OD, and the totalis OC.

Although it is unlikely that real-world finance ministers ever seriouslyponder a diagram like Figure 3.8, they are certainly aware of the consid-

118 chapter three

A

BO D CF

G A

1/α

Inflation taxLaffer curve

Olivera-Tanzicurve

Totalrevenue

Taxrevenues

Inflation rateP

P*ˆ

ˆFigure 3.8Inflation and othertax revenues.

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erations it includes. When the annual rate gets well into the double dig-its, the effects of inflation on a government’s ability to finance itself be-come a matter of serious policy concern.

So how do the economic authorities handle the inflation tax? Can it bedestabilizing? Many mainstream economists have addressed such ques-tions over the years—Bruno and Fischer (1990) summarize and extendtheir arguments. An alternative interpretation is offered here, ignoringOlivera-Tanzi effects and based on the analysis around Figure 3.7 above.

We stick with the Cagan money demand function (37) with m0 = 1 ina zero growth/zero interest rate economy, and assume that the govern-ment finances its nominal deficit P∆ only with monetary emission ,

∆ = /P = þm = þ exp(−α¾), (40)

using (36) and (37) to set up the various equalities. The final expressionfor ∆ is plotted as the “Inflation tax” schedule in Figure 3.9. Since ∆ =þ when the inflation rate is zero, ∆ itself pins the intercept of the curvealong the horizontal axis. The economy is assumed to satisfy (40) at alltimes so that for a given ∆, þ depends on ¾ or vice versa.

The “Steady-state” schedule (the 45° line along which þ = ¾) can in-tersect the Inflation tax curve at two, one, or zero points. The last case isanalogous to a nonintersection of the “Wage inflation” and “Indexingrule” curves in Figure 2.7; in the present context it represents a deficit

money, interest, and inflation 119

A C

A

B

B

Steady state

Inflation tax

Money growth rate

45°

Inflation rateP

∆ M

ˆ

ˆ

Figure 3.9The inflation tax andstationary equilibria.

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too big to be covered by the expedient of printing money. If the curves in-tersect twice, there are potential steady states with low and high inflationrates at points A and B on the “right” and “wrong” sides of the Laffercurve respectively.

What happens if the fiscal deficit suddenly increases at the low infla-tion steady state? To trace through the dynamic response we can main-tain the assumptions leading to equation (33) above to show that house-holds adjust their real balances according to the rule

~ = −α[exp(−α¾)]E(d¾/dt) = −αmE(d¾/dt), (41)

where as before E(d¾/dt) is the expected change in the inflation rate.Since ÿ = þ − ¾, we find that

E(d¾/dt) = (1/α)(¾ − þ). (42)

With myopic perfect foresight or E(d¾/dt) = d¾/dt, (42) amounts to a re-statement of (33). The principal difference between the present modeland Wicksell’s is that the latter contains an explicit macro framework forthe real side of the economy with the interest rate as a medium-run ad-justing variable according to the theory of loanable funds. Such an ad-justment scenario is conspicuously absent in Cagan-style models.

The effects of this limited specification show up clearly in Figure 3.9. Ifthe deficit ∆ shifts up, the Inflation tax curve (40) moves rightward andþ has to jump from point A to point C as monetary emission runs faster.But under myopic perfect foresight the Steady-State locus now repre-sents (42), building in unstable dynamics for ¾. Since C lies below thenew steady state at A′, both þ and ¾ will decline after þ jumps whilereal balances m steadily rise. Falling inflation and increased money de-mand are not supposed to happen when the government prints moremoney.

In Cagan’s day, monetarists got around this embarrassing outcome bypostulating “adaptive expectations” for the inflation rate. Later, whenrational expectations came in, this recourse fell out of fashion and themodel itself became less popular. Nevertheless, it still serves as the main-stay for the mainstream’s empirical analyses of inflation, for example,the World Bank studies presented in Easterly and Rodriguez (1995). Toillustrate how the model can be made to work with adaptive expecta-tions for changes in inflation, let a (for “acceleration”) stand for d¾/dtand ae = E(d¾/dt). The key hypothesis is that ae changes over time ac-cording to an error-correction mechanism,

±e = ρ(a − ae). (43)

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In rather plausible fashion households adjust their ideas about how in-flation is likely to change on the basis of the error in their present percep-tions (ρ is a constant describing their speed of adjustment).

Stability analysis for (43) is tedious but straightforward. Using (43),(42) can be restated as

¾ = αae + þ.

Differentiating with respect to time gives

a = α±e + dþ/dt.

Substituting this expression back into (43) and simplifying gives

±e = [1/(1 − ρα)][dþ/dt − ae]. (44)

The next step is to express dþ/dt in terms of growth of the fiscaldeficit d∆/dt. Since þ = ∆/m from (40), we have

dþ/dt = (1/m)(d∆/dt − ∆ÿ) = (1/m)(d∆/dt + ∆αae),

where the expression after the second equality follows from (41). Substi-tution into (44) and simplification using (40) give a final equation

±e = [1/m(1 − ρα)][d∆/dt + m(þα − 1)ae]. (45)

If the fiscal deficit starts to increase when the economy is at point A inFigure 3.9, then þ < 1/α since seigniorage is not being maximized. Thecoefficient on ae on the right-hand side of (45) will be negative. Then solong as money demand is not overly responsive to the inflation rate(small α) and/or expectations are sluggish (small ρ) the condition ρα < 1will hold and (45) will be a stable differential equation for ae. A growingdeficit d∆/dt drives up ae in (45). As the system arrives at a new steadystate with a = ae = 0 when d∆/dt returns to zero,29 from (42) the infla-tion rate itself converges to the new, higher level of þ. Monetarist sanityreturns, at the cost of a few tranquilizing assumptions to hold down thevolatility built into rational expectations.

Although it is not usually described in such terms, the last model to beconsidered can be viewed as an attempt to retool Cagan-type equationsinto a full macro system à la Wicksell. It gives rise to a “tight money par-adox” resembling the peculiar dynamics in Figure 3.9. The original ver-sion was developed by Sargent and Wallace (1981) in an opaque over-lapping generations setup; a simpler version provided by Liviatan (1984,1986) is adopted here.

The basic accounting appears in Table 3.2, including column (7) andcell B4. It is simplest to drop deposits D from the model and assume that

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the accounts of firms and households are consolidated into the handsof the latter. There is no growth, so investment g is zero. The govern-ment’s deficit (scaled to the capital stock) is ∆/K = γg + jB/K, with Bas the outstanding stock of inflation-indexed bonds that the authori-ties have placed on the market. Including bond finance is the step thatSargent and Wallace take beyond Cagan. The bonds carry a predeter-mined real interest rate j, perhaps set on the basis of time preference. Thefiscal deficit is financed by bond sales and money emission,

∆/K = À/K + /PK.

Liviatan solves an optimization problem to scale consumption andmoney demand to household real wealth Ω = M/P + B + K, consistentwith the full use of capacity presupposed in row (A) of the SAM with upredetermined. Without much violence to the data, it is simpler to usethe capital stock as the scaling variable for the demand functions,30

C = γhK and M/P = m = [(j − γh)/(j + ¾)]K. (46)

Assuming that the inflation rate is correctly observed, one can com-bine the money demand function in (46) with the relationships in (36) toget a differential equation for real balances,

~ = (j + þ)m − (j − γh)K. (47)

The government’s consolidated accounts give an equation for emissionof bonds,

À = −þm + jB + γgK. (48)

The Jacobian of (47) and (48) is

j +−

$

$M

M j0

It has two positive eigenvalues, so expect some fireworks.Assume that the economy is in an initial steady state, with ~ = À = 0

and þ = ¾. What happens if the government tries to switch from mone-tary to credit financing by reducing the rate of growth of the money sup-ply? The answer is pretty clear. From (47), the reduction in þ makes ~< 0. Because of the positive feedback in the equation, m falls over timeat an increasing rate. From the money demand function in (46) with theinterest rate j constant, the only way m can decline is through an increasein the rate of inflation, which induces people to hold lower real balances.So ¾ rises, at an increasing rate. This burst of inflation in response to

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tighter money is the first part of the “paradox.” It amounts to the Figure3.9 story with lower as opposed to higher levels of ∆ and þ.

A second stage follows from the bond market. In equation (48), thejump downward in þ makes À positive; the subsequent reduction in mand positive feedback accelerates the growth of B. Ultimately bond de-mand is supposed to saturate so that suddenly À = 0.31 Rewriting (48)gives þ = (1/m)[jb − À + γgK]. The only potentially free variable in thisequation is þ, so the jump down in À forces money supply growth tojump up. Somehow m stays constant during and forever after this earth-quake so a new steady state sets in with ~ = À = 0. To complete the par-adox, the inflation rate ¾ has to jump to meet the higher þ.

In sum, monetary contraction leads first to a steadily rising inflationrate and then a leap in ¾ to a new steady state that somehow maintainsitself despite the manifest instability built into (47)–(48). Rising interestrates, falling output, and even interest rate cost push into faster inflationare potentially important responses to tight money which the Sargent-Wallace paradox leaves out. Wicksell thought seriously about all three.

Some part of economic reality is conspicuously missing from the newclassical vision. It is time to turn to Keynes.

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chapter four

z

Effective Demand and Its Realand Financial Implications

Subject to strong caveats set out below about how volatile, subjective ex-pectations can destabilize all the behavioral relationships it includes (es-pecially liquidity preference and the marginal efficiency of capital), TheGeneral Theory’s basic model has a clear and simple causal structure.1 Itcan be illustrated as follows:

w PM

i ICYX

fromX C IY XC f Y

⇒⇒ ⇒ ⇒

= +== ( )

(1)

The linkages are easy to describe from left to right. The nominal wage wis the principal determinant of the price level P, through a price-cost rela-tionship of the sort discussed in Chapter 2. With the money supply Mpredetermined, real balances M/P (in non–General Theory terminology)set the interest rate i according to Keynes’s liquidity preference theory.Investment I follows as enterprises compare the interest rate with themarginal efficiency of capital that they see emerging from their portfo-lios of potential projects. Consumption C, real output X, and real in-come Y emerge from the material balance relationship X = C + I, theoutput-income mapping Y=X, and the consumption function C= f(Y).

After an initial review of Kaleckian macroeconomics, this chapter pre-sents the relationships underlying (1) in detail, concentrating on a ques-tion central to The General Theory: will wage reduction stimulate em-ployment? We then discuss some of the many reactions that Keynes’sgenerally negative answer provoked. These basically took two forms.One was a move to revise the causal structure (1) toward the “modern”version, in which real macroeconomic equilibrium is determined in thelabor market as in Figure 2.2 or Figure 4.4, rather than in the com-modity market that Keynes and Kalecki emphasized. At the same time,Keynes’s insights into financial markets were systematically repressed.The beginnings of these decades-long processes are examined here, andsubsequent high points are presented in Chapter 6.

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The second set of revisions aimed at putting macroeconomics on amore MIRA or Walrasian basis by emphasizing “micro foundations”of macro behavior and respecifying The General Theory’s consump-tion and investment functions. As the new Keynesian movement demon-strates, this effort is still in full swing. The story here begins with theideas behind The General Theory and goes on to currently popular for-mulations.

1. The Commodity Market

It is convenient to discuss Kalecki’s and Keynes’s approaches to the de-termination of commodity market equilibrium in sequence, beginningwith an updated version of the former because it is a bit simpler andleads naturally into the structuralist models discussed in Chapters 5 and7–10. Two basic questions are addressed: First, in an economy closed toforeign trade, do real wage increases cause effective demand to fall orrise? Second, if we take such linkages into account, do nominal wagecuts stimulate employment? Keynes’s answer to the second query was aresounding no, but the matter is still subject to intense debate.

The mode of argument is to impose different causal schemes on simplemodels, to ask which ones fit macroeconomic stylized facts and institu-tions the best. The starting point is Kalecki’s (1971) analysis of outputadjustment, with extensions independently due to Rowthorn (1982) andDutt (1984) regarding how changes in the real wage affect output, theprofit rate, and growth. A substantial literature has emerged in the wakeof their papers—see Blecker (2002a) for a survey.

As we observed in Chapter 1, Kalecki believed that commodity outputis not limited by available capital stock or capacity, and that final goodsprices are determined from variable costs (for labor only in the simplestmodel) by a markup rule:

P = (1 + τ)wb, (2)

where the notation is the same as in previous chapters: P is the pricelevel, w the nominal wage rate, b the labor-output ratio, and τ themarkup rate. We assume that w is fixed at any point in time, from in-stitutions and a history of bargaining or class struggle (Keynes’s ideasabout these matters were introduced in Chapter 2 and are extended be-low). For the moment, the coefficient b is assumed to be determined bytechnology and custom.

For a given money wage w, we concentrate on the macroeconomic ef-fects of changes in the real wage ω = w/P or the profit share π. Like w,both variables are determined by historical forces and policy interven-

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tions. The latter can range from tax/transfer policies through actionssuch as price and import controls to labor market regulation and nation-alization of firms. Shifts in distribution can be specified by changes in π,τ, or ω.

Any one of these parameters identifies the others. For example, 1 + τ= 1/(1 − π). We use this formula to restate the markup rule (2) as equa-tion (3) in Table 4.1, which is a compact rendition of Kaleckian macro-economics in an economy closed to foreign trade. Equation (4) expressesthe real wage in terms of the profit share. The output-capital ratio u(which as usual we take as a measure of economic activity) is defined by(5). The profit rate r is identically equal to the product of the profit shareand the output-capital ratio, equation (6).

Let gi stand for investment demand, expressed as the growth rate ofthe capital stock (ignoring depreciation, gi is the ratio of real investmentto capital). Kalecki assumed that gi depends on the profit rate r as an in-dex of expected future earnings. Kaldor (1940) and Kalecki’s colleagueSteindl (1952) introduced the output-capital ratio u as another variableaffecting gi. Its influence can be rationalized by the observation thatwhen the economy normally operates below full capacity, then a higherlevel of capacity utilization is likely to stimulate faster accumulation.Dutt and Rowthorn picked up on the Kaldor-Steindl formulation, writ-ing investment functions in forms similar to the one appearing after thefirst equals sign in (7). The expression after the second equality followsfrom (6), and the function gi = gi(π, u) with both partial derivatives posi-tive can be postulated as a general description of investment demand.

Let gs stand for the capital growth rate permitted by saving supply,that is, national saving divided by the value of the capital stock PK. In

126 chapter four

Table 4.1 Closed economy macroeconomic relationships

P = wb/(1 − π) (3)

ω = (1 − π)/b (4)

u = X/K (5)

r = πu (6)

gi = g0 + αr + βu = g0 + (απ + β)u = gi(π, u) (7)

gs = [sππ + sw(1 − π)]u = s(π)u (8)

gi − gs = 0 (9)

MV = PX or ω = wKu/MV (10)

u = u (11)

sπ = sπ(M/P); sw = sw(M/P) (12)

P = f(w, rP); b = L/X = fω(ω, r) ;1/u = K/X = fr(ω, r)

(13)

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(8), saving comes from markup and wage income at rates sπ and sw re-spectively. If workers don’t save (sw = 0), (8) reduces to the “Cambridgeequation” embedded (with sπ = 1) in Table 1.1: gs = sππu = sπr. Moregenerally, we have gs = s(π)u, with s(π) an increasing function of π whensπ > sw.2

Macro equilibrium based upon (3)–(8) occurs when excess commod-ity demand is zero, or (9) is satisfied. Before we use this equation to fig-ure out the effect on output of changes in the income distribution, aword should be added about the formulas in (10). They complete themodel with the simplest possible money market specification, omittinginterest rate effects to force a sharp contrast between structuralist andmonetarist views.

The main point is that the system (3)–(9) solves for all variables ap-pearing in (10) except M and V. The simplest Kalecki model presupposesendogenous money in the Banking School tradition discussed in Chapter3. Relative and absolute prices are being determined in the nonmone-tary part of the economy by institutional forces; therefore, M and/or Vmust be endogenous. It is easy to verify that proportional changes in ab-solute prices leave the real equilibrium unchanged, so that the model“dichotomizes” in the sense of Patinkin (1966).

An alternative approach is to assume that M is predetermined and Van institutional constant. Then for a predetermined real wage or incomedistribution, the money wage w has to be endogenous. This reading iscrucial to orthodox recommendations to cut money wages to raise out-put, and to impose tight money to slow inflation. In practice, proactivemonetary policy is usually only attempted in connection with aggressivestabilization packages, as in the United States under the lash of PaulVolcker’s interest rate hikes in 1979. Predictably, instead of rapidly slow-ing inflation, very tight money forced the economy into a prolonged re-cession. As is usually the case, the output and employment slump didfinally wring out inflation, but at substantial social cost.

For now, we take macro equilibrium to follow from (3)–(9) with wpredetermined and M and/or V tagging along from (10). The real wage isalso predetermined, and output (or the output/capital ratio u) adjusts toensure demand-supply balance. Standard arguments show that this sys-tem will be stable when investment responds less strongly than saving toan increase in output. Formally, the stability condition is3

∆ = sππ + sw(1 − π) − g ui > 0, (14)

where g ui is the partial derivative of the investment function with respect

to u. If this inequality is violated, short-run equilibrium will be unstable.

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For future reference, note that Harrod’s (1939) growth model can be in-terpreted as a dynamic extension of the unstable case. As discussed inChapter 5, his “knife-edge” of instability was sharp because of an accel-erator-based investment function with dgi/dt instead of gi as the left-hand-side variable.

To show the effect of a change in the profit share on output, we candifferentiate the macro-balance condition (9) to get

dud

g s s uiw

ππ π

=− −( )

∆. (15)

From (14), the denominator on the right-hand side is positive. Equa-tion (15) shows that income redistribution in favor of profits will stimu-late economic activity if workers have a relatively high saving shareand/or the effect of the profit share on investment is strong. From thelinearized investment function in (7), the latter condition applies whenthe profit rate coefficient α is big. Real wage cuts boost aggregate de-mand when saving propensities from different income flows are similarand/or investors react with agility to profit signals.

With regard to other key variables, one can show that the profit rate rrises with a higher real wage if β in (7) exceeds sw. Redistribution towardlabor stimulates consumer demand. A strong investment response tohigher consumption offsets the lower value of π in (6) with a higher u.This “win-win” distributional scenario runs directly counter to the in-verse wage/profit trade-off built into the prices of production and neo-classical cost function models of Chapter 2, and is an intriguing aspect ofKaleckian macroeconomics.

Similar reasoning applies to the capital stock growth rate. The sign ofdg/dπ is positive if αsw − β(sπ − sw) > 0. A lower real wage speedsgrowth in the absence of the accelerator. It slows the economy if the ac-celerator is strong (β >> 0) and saving from wage income is lower thansaving from profits. As discussed in later chapters, an extended versionof the present model arrives at steady-state growth upon convergence ofdynamic processes affecting the income distribution; the condition juststated signifies that the growth rate is “endogenous” in the sense that itdiffers across steady states.

As noted above, the ambiguous effects of real wage changes on out-put, the profit rate, and growth have been the subject of much recentdebate in the structuralist literature. Following Bhaduri and Marglin(1990), an output increase in response to redistribution toward labormay be called “stagnationist” or “wage-led”—redistribution favoring

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workers activates an otherwise stagnant system (in an example of the“paradox of costs,” to apply another label). The opposite case in whichoutput is “profit-led” also becomes “exhilarationist” as a natural pieceof jargon.

As we will see shortly, there is no certainty with regard to the shape orslope of the income distribution versus aggregate demand relationship,but one might “naturally” suppose that a higher profit share will stimu-late capital formation more strongly when the share itself is low, that is,α in (7) is an inverse function of π or a direct function of ω. If so, the“Output response” relationship between the real wage ω and the out-put/capital ratio u is illustrated by Figure 4.1, which reintroduces thecapacity utilization/real wage plane already used in Chapter 2. Macroequilibrium always lies somewhere along the curve—the activity level ispicked out by the profit share or real wage. As the schedule is drawn, theeconomy is wage-led for low values of ω and profit-led for high ones be-cause of stronger profit effects on investment as the real wage rises. Ofcourse there are other possibilities, such as wage-led growth at low levelsof capacity utilization (the 1930s?) and profit-led otherwise. This sce-nario would make the Output response curve look like an inverted U in-stead of the backwards C in Figure 4.1.

effective demand and its implications 129

Real wageω Output response

Output/capitalratio u

Figure 4.1Relationship betweenthe real wage andoutput with no ca-pacity constraint.

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2. Macro Adjustment via Forced Saving and RealBalance Effects

Mainstream authors often want to make production subject to an upperbound. In the basic version of Say’s Law for industrialized economies,the limiting factor is the supply of labor &, so that in equation (11) Ä =b&. This restriction appears as the vertical line for a “Capacity limit” inFigure 4.2. What are the implications in a Kaleckian model?

In the diagram, macro equilibrium lies on the thickened segments ofthe curves. The economy may operate below capacity either along thewage-led segment AB or in the profit-led range CD of the Output re-sponse curve. Along the segment BC, production constraints bind. Be-low full capacity, adjustment of output toward the relevant curve is usu-ally assumed to be rapid, as shown by the small arrows.

The interesting question is how demand is limited to supply when ca-pacity constraints start to bind, due for example to progressive incomeredistribution in a wage-led economy, expansionary policy which shiftsthe entire Output response curve to the right, or an adverse supply shockthat makes Ä drop. Three mechanisms are likely to be important in prac-tice—forced saving, real balance effects, or the inflation tax. In an openeconomy, changes in net imports can play a major role.

In the model of Table 4.1, forced saving kicks in when the capacity

130 chapter four

D

Z

C

A

B

Real wageω

Output/capitalratio u

Capacity limit

u

Figure 4.2Modes of adjustmentwith and without abinding capacity con-straint.

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constraint (11) is added to the preceding equations. There is a standardoverdetermination problem with one more equation than there are vari-ables. This problem resolves itself, however, insofar as an incipient ex-cess of aggregate demand over capacity makes prices rise. If the moneywage is not fully indexed to inflation, the markup τ and profit share π in-crease, becoming endogenous, equilibrating macroeconomic variables.The real wage falls, reducing demand, output, and very possibly the rateof capital stock growth in a wage-led system.

This form of short-run inflationary adjustment via workers’ forcedsaving toward limited capacity is stable in the wage-led case—the seg-ment BZ in Figure 4.2.4 If the economy is profit-led—segment ZC—priceincreases raise profits, stimulate investment, and lead toward hyperinfla-tion in response to an initial increment in demand. Harrodian instabilityshows up in divergent prices instead of output levels.

Although it still hovers in the background, forced saving lost its starrole in mainstream macroeconomics between 1930 and 1936, the re-spective publication years of Keynes’s Treatise on Money and GeneralTheory (perhaps in line with the shift in the business cycle from price to-ward quantity variations, as discussed in Chapter 3). Much macroeco-nomic discourse, however, centers around an inverse relationship be-tween the price level and real effective demand (the “aggregate demandcurve”) of the sort that forced saving provides. When such a linkage wasagain needed after the Great Depression, it found its mainstream ratio-nale not in real wage reduction, but in lower real wealth.

The real balance or quantity theory explanation for the inverse price-demand relationship is an essential component of the orthodox argu-ment for cutting money wages to stimulate employment, as we will seein section 3. Its prominence helps explain the disinterest in differentialsaving propensities across income classes that most post–World War IIeconomists have displayed (recent exceptions are mentioned in sec-tion 12).

The adjustment scenario resembles the inflation tax, but with a jumpin P instead of ¾. An initial price increase when capacity limits arereached will reduce real balances or the money stock divided by the pricelevel. With the real value of their assets cut back by this change, wealth-holders save more to compensate, cutting consumption. From an invest-ment function like (7), capital formation follows in train.

The real balance process runs parallel to forced saving. In practice, thetwo modes of adjustment are hard to tell apart. In the model world,however, the real balance effect is easy to incorporate by adding (12) tothe full capacity specification. The saving rates sπ and sw become in-verse functions of M/P, the real value of the nominal money stock M. But

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P is directly related to τ and π (a higher markup goes together withhigher prices and lower real balances), so the saving rates rise with π.Another negative term −u[π(dsπ/dπ) + (1 − π)(dsw/dπ)] shows up in thenumerator of (15). Profit-led adjustment to distributional changes be-comes more likely, since markup increases cut demand by reducing bothreal wages and wealth.

Another way to evade capacity limitations is to bring in importsfreely—such a move could be treated formally in the model structurehere by including imports relative to capital stock as one more negativeterm in (9). Macro adjustment via wholesale importation has been im-portant in practice (recall France under early Mitterrand where house-hold durable goods highly prized by wage earners led the import surgeafter progressive redistribution, the United States under Reagan’s expan-sionary fiscal policy and Clinton’s household consumption boom, andcountless external crises in the Third World) and no doubt will remain soin the future.

3. Real Balances, Input Substitution, and Money-Wage Cuts

So far, wage cutting is no panacea. If capacity limits don’t bind, policiesaimed at shifting the income distribution in favor of profits may well re-duce output and employment. When the economy tends toward demandlevels exceeding capacity, real wage reductions induced by inflation mayhelp restore equilibrium, but will be less necessary when real balance ef-fects are strong.

In view of these observations, why does wage restraint remain a cen-tral orthodox theme? At least as far as output responses are concerned,the answer hinges on positing the real balance effect as the unique or atleast dominant macro adjustment mechanism, in conjunction with neo-classical input substitution. Building on Pigou (1943), Patinkin (1966) isthe central text in this regard. The work it summarizes established the“neoclassical synthesis” (or “bastard Keynesianism” in Joan Robinson’sphrase) that flourished through the early 1960s and pointed the way to-ward the monetarist and new classical revolutions that followed. NewKeynesianism can be viewed as a high-tech attempt to steer the profes-sion back toward an imperfectly competitive version of Patinkin.

To see the logic, we proceed by stages, first recalling that Keynes inThe General Theory was adamant in insisting that cutting money wageswould not effectively raise employment. He presented arguments alongtwo lines.

We have already encountered the first in connection with Dunlop’swage contours and the Taylor inflation model in Chapter 2. It was es-

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sentially practical (“not theoretically fundamental” in Keynes’s words).Wage reductions have to be made in piecemeal fashion, but each such at-tempt would be resisted by the affected group because not only its realbut its relative income position would be eroded. Even if, as Keynes ac-cepted in The General Theory, a lower economy-wide real wage is essen-tial to stimulate employment, “wage-wage” conflicts will make this goalvery difficult to achieve by negotiated contract revisions.

The second argument is that at least insofar as its first-order effectsare concerned, cutting the money wage cannot result in real wage reduc-tion. This result is easy to see in a Kaleckian model. In light of themarkup equation (1), such a change does not affect the output level.Prices just fall in proportion to wages, the profit share and real wage areunchanged, and macro equilibrium remains wherever it was along theoutput response schedule in Figure 4.1.

The General Theory differs from Kalecki by building in the “first clas-sical postulate” that the real wage equals the marginal product of laborunder a regime of decreasing returns to additional employment. Follow-ing the analysis in Chapter 2, a contemporary way to fit this view intoour equations is to drop the markup rule (3) of Table 4.1, and use theneoclassical supply specification appearing in (13) instead. This moveamounts to replacing imperfect competition in the product market and aconstant marginal (= average) product of labor with perfect competitionand a marginal product that falls when output rises. In (13), P = f(w, rP)is a linearly homogeneous cost function consistent with an aggregateproduction function having constant returns to scale in capital and la-bor. As we have seen, it can be restated as a wage-profit frontier in theform f(ω, r) = 1. Input demands follow from Shephard’s Lemma, wherefω and fr stand for partial derivatives.

To see how the argument works, assume for a moment that the realbalance effect is inoperative. In terms of the real wage ω, the macro bal-ance equation (9) can be written as

gi(ω, u) − [sπ − (sπ − sw)ωb]u = 0, (16)

where the profit share π can be replaced by the real wage in the invest-ment function since one depends monotonically on the other along thewage-price frontier. Equation (16) is a restatement of the Output re-sponse curve, redrawn in Figure 4.3.

As observed in Chapter 2, this model also implies an inverse relation-ship between the output-capital ratio and the real wage. Lower laborcost means that more workers can be profitably employed, leading u torise. This linkage underlies The General Theory’s real-side macro clo-

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sure. It combines (13) with (4)–(10) in Table 4.1. For the moment, we re-tain the hypothesis of passive money.

The graphical solution is instructive. The negatively sloped “Labor de-mand” curve representing (13) in Figure 4.3 uniquely picks out macroequilibrium, determining output and the real wage. Shifts in the Outputresponse schedule (from changing investment demand or fiscal moves)modify the equilibrium position. Higher effective demand moves theschedule to the right, causing employment to rise and the real wageto fall. Reducing the money wage has no effect in this formulation pre-cisely because the real wage is determined in Figure 4.3. A lower wmakes P drop in proportion, given effective demand. In a nutshell, this isKeynes’s “theoretically fundamental” argument against the power ofmoney-wage cuts.5

The conclusion does not depend on the slope of the Labor demandschedule, as Keynes (1939) admitted after Dunlop and Tarshis showedthat the real wage rose with output over the business cycle. As discussedin Chapters 7 and 9, extrapolating such a cyclical result to a steady-staterelationship of the sort depicted in Figure 4.3 is not a foolproof maneu-ver. But subject to this reservation, Keynes was willing to scrap the firstclassical postulate and accept a positive association between the realwage and output as an empirical likelihood, so long as his reasoningabout money wage changes went through.

Now we can reintroduce the real balance effect, which makes the sav-

134 chapter four

Real wageω

Output/capitalratio u

Output response

Labor demand

Figure 4.3Keynesian determi-nation of output andthe real wage.

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ing rates sπ and sw functions of real balances M/P, not the real wage w/P.Cutting the money wage reduces P through the cost function, raises M/P,and stimulates demand since wealth-holders feel richer. If the linkage isstrong, Keynes’s effective demand argument is undone (leaving out inter-est rate effects, which are brought in below).

Strong assumptions about model causality and empirical legitimacyare built into the real balance story. The causal question is whethermoney supply M is determined prior to the price level P. As noted inChapter 3, there is no historical dearth of eminent economists willing toargue that endogenous rather than active money may usually be the rule.The empirical doubt is whether the postulated positive effect of pricechanges on saving rates in (16) overrides the other linkages in that equa-tion.

The standard mainstream model answers both queries in the affirma-tive, dropping effective demand. In a popular stripped-down version, thequantity theory of money is transferred from the asset market to the realside of the system, and pressed into action as a shorthand representationof dominant real balance effects in demand. The model comprises equa-tions (4)–(6), the second version of the quantity equation in (10) withpredetermined M and V, and (13). Effective demand equations such as(7)–(9) don’t get around much any more.6

In this setup, it is easy to verify from (10) that for a given money wage,the real wage increases along with capacity utilization. Higher outputmeans that the price level must fall (and real wage rise) from the equa-tion of exchange. The direction of macro causality is the reverse of theone pursued heretofore. It supports a “monetarist wage-led” theory ofaggregate demand.

Equation (10) appears as the “Velocity” schedule in Figure 4.4. Itscross with the Labor demand curve (the same as in Figure 4.3) deter-mines macro equilibrium. The new twist is the dependence of the Veloc-ity relationship in (10) on the money wage w. Cutting w shifts the curvedownward to the dashed position, reducing the real wage and raisingoutput. A bigger money supply also leads u to rise and ω to fall be-cause of a higher price level. With their relative importance dependingon how easily new workers can be utilized (that is, on the value of a pa-rameter like the elasticity of substitution), both employment gains andforced saving play roles in adjustment to the bigger money supply. As al-ready observed in Chapter 3, over a period of fifty years, mainstreammacroeconomics returned very close to post-Wicksell/pre-General The-ory views about how equilibrium is attained.

In a preview of the mainstream models developed in Chapter 6, wecan also sketch how the return extends to the long run, with a “natural”

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rate of employment replacing Wicksell’s rate of interest. It is easy to turnFigure 4.4’s short-run adjustment into a process leading to the naturalrate in steady state, following Friedman (1968) and later Fischer (1977)and John Taylor (1980). Suppose that for reasons of “expectationalerrors” (Friedman) or “staggered contracts” (Fischer and Taylor), themoney wage responds to labor market disequilibrium according to aPhillips curve differential equation such as

¢ = h(bu − ×), (17)

in which bu is the current labor/capital ratio, and × is the ratio corre-sponding to zero wage pressure or the natural rate.

For a given capital stock, employment is an inverse function of w fromFigure 4.4. The implication is that if bu drops below ×, then w begins tofall, leading to real wage reduction, new hiring, and restoration of equi-librium at bu = ×. At this long-run stable position, u is at its natural ratelevel and ω comes from (13). Hence from (10) the money wage is also de-termined. All nominal prices follow from MV = PX; there is no room ina monetarist steady state for institutional influences on either the real orthe money wage. Macroeconomic adjustment relying on real balance ef-fects is institutionally overdetermined.

This observation harks back to the discussion of “nominal anchors”

136 chapter four

Real wageω

Output/capitalratio u

Velocity

Labor demand

Figure 4.4The effect of a money-wage cut when ag-gregate demand isdetermined by theequation of ex-change.

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for the price system in Chapter 2. In the monetarist long run of Fig-ure 4.4, the money supply is the anchor; through the cost function themoney wage must adjust to ratify the price level emerging from the equa-tion of exchange. In his preferred short run, Keynes reasoned in exactlythe opposite direction. Institutional forces in the labor market don’t nec-essarily hold the money wage constant, but do dictate how it varies overtime. The price level follows from the cost function, and the role ofthe policy-determined money supply is to regulate the interest rate andthereby effective demand. Just how this is supposed to happen is thetopic we take up next.

4. Liquidity Preference and Marginal Efficiency of Capital

Go back to scheme (1). Keynes’s treatment of the interest rate and invest-ment demand determines its linear causal chain. He forged it in the early1930s after breaking away from the natural rate theory of Wicksell andthe Treatise on Money.

Reading left to right in (1), a key link ties investment I to the interestrate i. In fact, there are at least two distinct investment models in thebook: the “marginal efficiency of capital” (MEC) story in Chapter 12and a much more interesting discussion of asset pricing in Chapter 17,sketched in section 8 below.

MEC analysis is pretty standard. It follows from Keynes’s mentorMarshall and the profitability calculations characteristic of Irving Fisher.Each firm is supposed to have a schedule (probably a step function) witha generally negative slope relating the expected return on investmenton the vertical axis to the volume undertaken on the horizontal. The firminvests until the rate of return on its “last” project falls to the marketrate of interest. Aggregating across firms gives the economy-wide MECschedule.7 If rate of return and interest rate do not get fully equalized (fora variety of “frictional” reasons), then the investment demand function(7) in Table 4.1 extends naturally to the form

gi = g0 + αr + βu − θi, (18)

which we have already met (without the accelerator term βu) in connec-tion with the Ramsey model in Chapter 3.

Like all algebra, (18) elides a major theme in Keynes’s thought—theexistence of fundamental uncertainty. Its essence is best seen using thedistinction drawn by the early Chicago economist Frank Knight (1921)between “risk” and “uncertainty.” Probability distributions can be as-

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signed for risk; human knowledge is insufficient to apply probability cal-culus to much of our future prospect, which is truly “uncertain.”8

The General Theory and follow-up contributions such as Keynes(1937a) are replete with eloquence (some reproduced below) about howthe “dark forces of time and ignorance” require that investment de-cisions be undertaken in conditions of fundamental uncertainty inKnight’s sense. Therefore, the “expectational” element in investmentlooms large. In algebraic terms, r in (18) should be replaced by an ex-pected profit rate re with properties that cannot be formalized, the inter-cept term g0 can jump up or down unpredictably as “animal sprits”change, and so on. For computation of economic prospects even in thenear future, there is no reason to expect the parameters in an investmentfunction like (18) to be stable or even well defined.

The same observations apply to the “liquidity preference” relation-ship which determines the interest rate from the real money supply M/P.The formal part of the story is that demand for real money has twocomponents. The first is for “transactions,” proportional to the level ofoutput X or capacity utilization u along the lines of the equation of ex-change (another hand-me-down to Keynes from Marshall). “Specula-tive” demand, on the other hand, depends inversely on the rate of inter-est i. Keynes rationalized its existence by invoking the market for bonds(an institutional feature that may or may not be present in any giveneconomy).

The simplest version of the argument rests on the well-known inverserelationship between the price of a bond and its current interest rate (dis-cussed in detail in the following section). Suppose that somebody ex-pects the interest rate next “period” to be higher than it is now, so thatthe bond price is necessarily expected to be lower at that time. Then ifthe player buys a bond today, she or he will anticipate a capital loss thatmay be big enough to offset the bond’s coupon payment. Given the lowcurrent interest rate, it may be wiser not to buy at all, and stay “liquid”by holding money instead. After all, the bond is expected to cost less inthe future.

At worst, this narrative suggests that the interest rate is at the level it isbecause it isn’t at another. A more generous interpretation is that liquid-ity preference involves “bootstrap” dynamics whereby the “tone andfeel” of the financial market evolve over time, with changing percep-tions about future interest rates affecting current preferences for liquid-ity. There may or may not be a steady-state “natural” interest rate as acenter of gravitation for this process. Keynes’s pronouncements on thispoint were Delphic, for reasons to be discussed in the following sections.

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But he was clear that like investment demand (18), the money demandfunction

M/P = µ(X, i) (19)

is not going to be notably stable over time.A final comment is that a specification like (19) marks a significant

break from previous analysis by relating the interest rate and rates of re-turn more generally to stocks of real and financial claims rather thanflows of the sort built into real and loanable funds theories. Beyondliquidity preference, moving from a flow to stock formulation for fi-nancial analysis ranks with the principle of effective demand as one ofKeynes’s greatest contributions in The General Theory. Tables 1.4 and1.5 show that outstanding liabilities of the business sector and govern-ment are about two times GDP. Many of these securities turn over everyday, and derivative contracts effectively make the turnover of outstand-ing paper many times larger. Bringing these transactions in stocks intothe purview of macroeconomics was a major accomplishment.

5. Liquidity Preference, Fisher Arbitrage, and theLiquidity Trap

Thinking about financial markets in terms of stocks, in particular stocksof bonds subject to capital gains and losses, raises many analytical ques-tions. One set came to the fore in the 1990s in policy debates about therelevance of Keynes’s “liquidity trap” to issues such as the effects on in-terest rates of changing inflation rates, for example, in Japan’s “post-bubble” economy. A flash forward makes sense before we summarizeThe General Theory’s central messages in section 6, and go on to main-stream reactions thereto.

Kregel (2000) points out that there are at least three theories of the li-quidity trap in the literature—Keynes’s own analysis in Chapter 15 ofThe General Theory, Hicks’s glosses in his 1936 and 1937 reviews of thebook, and a view that can be attributed to Irving Fisher in the 1930s andPaul Krugman (1998) in latter days. We will take these alternatives in or-der, devoting the most space to Keynes. His central question was abouthow prices of long bonds react to changes in their interest rates. Aspointed out above, an investor is likely to opt for “liquidity” or holding(something like) money as opposed to a long bond if she or he expectsthe relevant interest rate to rise, causing a capital loss on the bond thatmay exceed the interest or “running yield” it will provide.

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To make this insight more precise, we can work through the details fortwo sorts of bonds—”consols” (a nickname for British government secu-rities resulting from a loan consolidation in 1751) which promise to paya coupon value of one dollar in perpetuity and “zeros” with no couponbut which will be redeemed at face value upon maturity. Zeros therebysell at a discount until they can be cashed out. The relevant interest ratesare ic and iz respectively. For reference, the short-term nominal and realrates are i and j respectively. For Fisher and Krugman, in particular, jamounts to a natural rate emerging from the market for loanable funds.

In continuous time, the value C of a consol is

C=∞

∫exp0

(−ict)dt = 1/ic. .

The question at hand is how C changes in response to a shift in ic. Thelog-derivative (called “modified duration” in finance jargon, as an indi-cator of the “length” of the bond’s payment stream) is

dC/C = (−1/ic)dic. .

Keynes was interested in how a change in ic would affect the return Rc

to holding a consol for a short time δ. From the equation just above, theanswer turns out to be

Rcδ =( )

( ) ( )i C dC

Ci

dCC

idi

ic

c cc

c

+= + = −

δδ δ1

2. (20C)

Formulas like the one to the right are sometimes called “Keynes’s squarerule” after a notably obscure numerical example on p. 202 of The Gen-eral Theory. Obscurity notwithstanding, its conclusion is worth quoting:“If, however, the rate of interest is already as low as 2 per cent, the run-ning yield will only offset a rise in it of as little as 0.04 per cent per an-num. This, indeed, is perhaps the chief obstacle to a fall in the rate of in-terest to a very low level. . . . [A] long-term rate of interest of (say) 2 percent leaves more to fear than to hope, and offers, at the same time, a run-ning yield which is only sufficient to offset a very small measure of fear.”At ic = 0.02 (or something similar), the risk of capital loss due to beingilliquid is very high if the rate is one day expected to rise to a “normal”level, while the return itself is very low. Hence most investors will al-ready be liquid and the rate is unlikely to fall much further.

The story is broadly similar for a “zero” held at time zero and matur-ing at time T. Its value is

Z = exp(−izT).

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The analog to (20C) is

Rzδ = iz(1 −Ti

diz

z )δ. (20Z)

Note that the coefficient on −diz/iz is T which will be “large,” in manycases more than 10. By the square rule, the same observation applies tothe coefficient 1/ic on −dic/ic in (20C).

On the basis of these examples, let il stand for a generic long rate andE(dil) be its expected change. If the ongoing inflation rate is ¾, Fisher-style arguments about time preference combined with liquidity prefer-ence suggest that under near-perfect arbitrage il should satisfy a relation-ship such as

il[1 − (φ/il)E(dil)] = ρ + i = ρ + j + ¾, (21)

in which ρ is a “risk premium” on long bonds that would equal zerounder long-range completely perfect foresight. As in (20C) and (20Z)the coefficient φ/il multiplying the expected change in the long rate is“large.”

Three conclusions follow.First, for a given inflation rate, E(dil) > 0 means that asset-holders will

think twice about investing long. The equality in (21) could easily be vio-lated, with the left-hand side being less than ρ + i or ρ + j + ¾ and verypossibly negative. This is the essence of liquidity preference, at least withregard to holding bonds.

Second, if arbitrage rules and equality holds in (21), a jump in the in-flation rate will not be met by a proportional increase in il if E(dil) ≠ 0.As stressed by Kregel (2000), Fisher arbitrage does not apply in generalto long rates and one has to tell a more complicated story. An example ispresented momentarily.

Finally, a “normal” yield curve is characterized by the inequality il >i—long rates are generally higher than short. The main observed excep-tion for the U.S. economy is a flat or inverted yield curve in advance ofthe onset of recession (Estrella and Mishkin 1996), due mainly to up-ward movements in short rates. A typical regression equation takes theform il = α + βi, with α having a value of a few hundred basis points (afew percentage points) and β a bit less than one. From (21), the risk pre-mium ρ is small and the implicit expectation underlying a rising curvemust be E(dil) > 0. However, given the likely magnitude of the coef-ficient φ/il and the fact that β is close to one, the anticipated upward driftin il need not be brisk.

From a contemporary perspective, it is tempting to use (21) in a dy-

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namic context to analyze the interactions of the interest and inflationrates. Naturally, this is done assuming myopic perfect foresight or E(dil)= dil.9 Setting ρ = 0 for simplicity, we get a differential equation for il,

dil/dt = (1/φ)(il − ¾ − j). (22)

Unsurprisingly, the positive effect of il on its time-derivative makes (21)unstable. However, the interest rate response to a shock to the right-hand side will be sluggish since the coefficient 1/φ will be “small.” Inpractice, long rates tend to be substantially less volatile than shorts.

In a stripped-down model, it is simplest to assume that the time-deriv-ative of the inflation is observed perfectly, and satisfies

d¾/dt = −ηil − v¾ + Γ. (23)

The coefficient η would normally be assumed to be positive but small—an increase in the long rate would slow inflation by reducing aggregate(especially investment) demand but the effect might not be very strong. Ifv > 0 inflation tends to be self-stabilizing, and Γ represents an infla-tionary shock. It is easy to verify that the Jacobian of the system (22)–(23) has a negative determinant and an ambiguously signed trace—weare back in saddlepoint country with il as the jumping variable. Thephase diagram appears in Figure 4.5.

142 chapter four

Inflation rateP

A B

C

S

S

Long-terminterest rate

il

Stableinterest rate

Stableinflation

ˆFigure 4.5Dynamics of long-term interest andinflation rates.

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Suppose the system is initially at point A, but then Γ increases so thatthe Stable inflation locus along which d¾/dt = 0 shifts upward. The newequilibrium is at C, where the inflation curve intersects with the Stableinterest rate curve along which il = j + ¾ and dil/dt = 0. As illustrated,the dynamics involve an upward jump of il from A to B, and then asteady increase in both variables to the new steady state (at which, a bitunrealistically, there is a flat yield curve with il = i).10 Reading the dia-gram in reverse, a deflationary shock would cause il to jump downward,and then both variables would decline. Either way, although in a stan-dard rational expectations (and bond market?) narrative the interest ratejumps in anticipation of an oncoming inflation or deflation, it under-shoots in the sense that it does not immediately arrive at its new equilib-rium level.

We will return to the policy implications of Figure 4.5, but first a fewwords about the two other interpretations of the liquidity trap men-tioned above. In his first review of The General Theory, Hicks (1936)saw a stable value of the interest rate as requiring an elastic supply ofconsumption goods (in other words, output is the macroeconomic ad-justing variable) and an elastic supply of money at some (low) level of i.In the IS/LM diagram that Hicks (1937) introduced in his second re-view, the LM curve will have a horizontal section that may coexist withlow levels of u and i “on the left side” of the picture. For an example,see Figure 4.7 below. With low effective demand and the flat LM sched-ule, monetary policy becomes ineffective—the traditional metaphor is“pushing on a string.”

In postulating an elastic money supply (at least at a low rate), Hicksjoined hands with the Banking School and the post-Keynesians but wasnot wholly consistent with Keynes, as the latter pointed out in corre-spondence. On the other hand, the horizontal LM segment is a visuallystriking way of representing the flight to liquidity that can ensue when il

is low, E(dil) is positive, and the expression on the left-hand side of (21)has a value close to or less than zero.

The Fisher-Krugman theory can be illustrated with the standard loan-able funds diagram in Figure 4.6. Saving and investment are supposed todepend on the real return to capital j, which by Fisher arbitrage in turnshould be equal to i − ¾. For historical reasons investment demand mayhave declined (shifted left) and saving supply increased (shifted right) tosuch an extent that they only intersect at a negative real rate jtrap. Thenominal rate i, however, can only fall to zero. To get a negative real rateand raise investment, the only recourse is to increase the rate of inflationwith the nominal rate somehow held constant to make i − ¾ < 0. Suchwas Fisher’s advice to President Franklin D. Roosevelt in the 1930s and

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Krugman’s to the Japanese central bank sixty-odd years later. Moreover,according to Krugman the bank has a credibility problem in that it trulyhas to make an effort to emit money in increasing volume over time toset off a Cagan-style inflationary process. A simple once-off increase willjust make P jump from the equation of exchange and not force ¾ to be-come convincingly positive.

With regard to practical matters, Keynes himself saw the appearanceof a true liquidity trap as hypothetical: “whilst this limiting case mightbecome practically important in the future, I know of no example of itheretofore” (p. 207). Suppose we take Japan as the “future example.”What can be said with regard to policy?

The traditional “Keynesian” recommendation is to take advantage ofthe horizontal LM segment by boosting aggregate demand. In Japan be-ginning in the 1990s, after a period of highly contractionary monetarypolicy aimed at deflating the 1980s asset price bubble once and for all,such efforts took the form of fiscal expansion in an economy in whichdemand had historically been export-led. One important outcome wasa big increase in the fiscal debt/GDP ratio—a potential stock/flow dis-equilibrium of a sort not addressed by Keynes but of great concern tosuccessors such as Wynne Godley (see Chapters 1 and 8 herein). If thegovernment has become debt-constrained and export growth prospects

144 chapter four

Real interestrate j

Saving,investment

I(j) S(j)

jtrap

0

Figure 4.6A Fisher-Krugmanliquidity trap.

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are limited, then boosting consumption demand is the only remainingoption. It may or may not be possible to convince Japanese householdsto save less and thereby boost demand (a linkage sometimes called the“paradox of thrift”), but in analytical terms their spending behavior hasno direct connection with a liquidity trap. Keynes, to be sure, did see ahigh national saving rate and a yearning for liquidity as a combined rec-ipe for stagnation. More on that in Chapter 8.

Inducing inflation also has its complications, on rational choicegrounds. If Fisher arbitrage happens and the right-most equality holds in(21) with the real rate j taking a value somewhere between Figure 4.6’sjtrap and zero, then any successful attempt to raise ¾ will simply increase ias well, leaving the real return to investment unchanged. This is, after all,the traditional quantity theory story about how the nominal interest rategets determined. Furthermore, the rational expectations extension of(21) to the dynamic system (22)–(23) suggests that the nominal long rateil will jump in anticipation of any future inflationary process, inflictingcapital losses on long bonds and raising the short-term cost of financinginvestment projects, thereby making the current effective demand short-fall worse. For an economy successfully to inflate its way out of a liquid-ity trap, the monetary authorities would have to be able to control boththe short and the long segments of the nominal yield curve (as well as,one might add, the volume of capital movements across their borders). Itis not obvious that the Bank of Japan could or ever would choose towield such extensive powers.

6. The System as a Whole

Perhaps it is a relief to turn from the late-twentieth-century problems ofJapan—with clear Keynesian characteristics but no obvious solutions—to ask how The General Theory’s model hangs together. Using equationswritten out above, a revised version of the causal chain in (1) takes theform:

w PM

i gs s

i

w

⇒⇒

⇒⇒

from from (18)from (12) g( )

,19

πs from (8)

⇒ u from (9). (24)

Besides feedback effects of X or u (and r = πu) in (18) and (19) whichare taken up in section 7, (24) incorporates two major changes in com-parison with (1). First, a lower nominal wage causes the price level tofall, the real money stock M/P to rise, and thereby savings rates sπ and sw

to decline—this is the real balance effect. Second, via the liquidity pref-erence relationship (19), a higher level of M/P will drive the interest

effective demand and its implications 145

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rate down, stimulating investment demand through the “Keynes effect.”Nominal wage reductions stimulate effective demand and employmentin two ways, contrary to a central tenet of The General Theory. Whathas gone wrong?

“Very little,” the Master might reply. Keynes did not mention the realbalance effect in The General Theory. If he had, he almost certainlywould have dismissed it as a theoretical curiosum with scant empir-ical relevance. As discussed in section 10, the significance of wealthchanges for saving and consumption decisions remains controversial tothis day, especially in the Keynesian short run. The American stock mar-ket plunges of 1987 and 2000–2001 did not reduce aggregate consump-tion visibly, although they did cut back on sales of yuppie artifacts like$30,000 imported cars.

Keynes’s counterargument to his own “effect” is that cutting moneywages to reduce prices to reduce interest rates to stimulate investmentdemand is a tricky maneuver. The first lesson that every applied econo-mist learns is not to give a lot of credence to long causal chains. Why notjust increase the money supply directly? This is in fact his recommenda-tion in Chapter 19 of The General Theory.

In sum, based on thoroughly neoclassical production theory and theprinciple of effective demand, the first-order argument in The GeneralTheory is that reducing nominal wages will not successfully stimulateemployment. Two distinctly second-order arguments (one introduced byKeynes himself) go the other way. Insofar as any debate in economicscan be settled a priori, one might think that Keynes had won.

Posterity, however, judged differently, reversing the priority of the ar-guments just mentioned. Less than a decade after The General Theorywas published, we find Modigliani (1944) observing that “it is the factthat money wages are too high relative to the quantity of money that ex-plains why it is unprofitable to expand employment to the ‘full-employ-ment’ level” (emphasis added).

Why are wages “too high” instead of the money supply “too low”?One answer is that an economic expansion induced by increasing Mmight well be more inflationary than one resulting from a lower w.With rising prices, debtors would benefit and the real wealth of creditorswould go down. Regardless of the motives behind the young FrancoModigliani’s choice of wording six decades ago, it is pretty clear onwhich side of the debtor/creditor divide the majority of the economicsprofession would like to (and probably does) reside. Their preference fordeflation over (moderate) inflation is in part class-determined, a thoughtdeveloped further in Chapter 7.

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7. The IS/LM Model

The missing elements in the discussion just concluded are the effectsof changes in the output/capital ratio u and profit rate r on money de-mand in (19) and macroeconomic balance in (9). Such linkages were firstbrought into an explicit model with the celebrated “IS/LM” formulationof Hicks (1937), who also threw in a positive effect of the interest rate onsaving for good measure.

IS/LM can be interpreted in many ways. One (voiced at times byKeynes) is that it is not a bad representation of at least the formal side ofThe General Theory. Another, expressed for example by Pasinetti (1974)and the papers in Eatwell and Milgate (1983), is that Hicks’s machineperverts Keynes’s vision by turning its clear causal structure into a mushyset of simultaneous equations while ignoring the social structures, in-complete information, and potential financial instability that are at itsroots (perceptions that, in writing much later, Hicks (1980–81) seemedto share). In this reading, the underlying thrust of IS/LM effort was toturn The General Theory into an empirically dubious Special Case.

Be that as it may, it is still important to get Hicks on record. Onthe LM side of the economy, the presentation here is based on Tobin’s(1969) approach to financial modeling. Tobin is faithful to Keynes indetermining rates of return in markets for stocks of assets and liabili-ties. However, Tobin-style models like the one to follow usually take aSpecial Case or Walrasian tangent by adopting the “full employment”Modigliani-Miller (1958) financial market specification discussed inChapter 1. Financial markets are cleared solely by adjustments in assetprices and rates of return (for alternative perspectives, see the followingsection and Chapter 8). By way of compensation for a super-orthodoxLM as well as to avoid the complications introduced by the “first classi-cal postulate,” we then set up the price/quantity or IS side of the systemalong Kaleckian lines.

Table 4.2 presents balance sheets for the main financial actors. Thewage earners and rentiers of Table 1.3 are consolidated into “house-holds.” Their portfolios contain money M, bonds or “T-bills” Th emittedby the government, and the value of business equity PvV. Followingcontemporary convention, bonds are treated as very short term (“over-night,” say), so they pay only a running yield and we do not need tocarry their price in the accounting. The benefit is convenience, at the costof leaving out Keynes’s liquidity preference rationale for holding moneyin the first place. Households’ wealth Ω is the sum of their asset hold-ings: Ω = M + Th + PvV (note that V now stands for equity and not ve-

effective demand and its implications 147

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locity). Households, business, banks, and so on are assumed to satisfysuch restrictions at all times—there are no “black holes” in their balancesheets.

The asset value of business capital stock is qPK, with PK as replace-ment cost. Securities issued by business comprise equity and loans frombanks L, and the sector’s net worth is set to zero. The valuation ratio is“average q”: q = (L + PvV)/PK. Commercial banks lend to firms and is-sue money. Their reserve against deposits or “high-powered money,” H= M − L, takes the form of claims on the central bank. The offsettingcentral bank asset is held as T-bills Tc, where T is the government’s out-standing liability with a market-clearing condition

Th + Tc = T.

The central bank can expand the stock of high-powered money by buy-ing T-bills from households. The purchase drives up notional bondprices in the very short run, and thereby reduces the T-bill interest rate i.

Even highly aggregated financial systems like the one in Table 4.2 needa wagonload of symbols and equations to analyze. To begin with ac-counting, first note that consolidating entries across balance sheets andimposing the market-clearing condition for bonds shows that “primarywealth” in the system is

Ω = qPK + T, (25)

all ultimately held by households. As rationalized in Chapter 6, theModigliani-Miller theorem says that businesses have zero net worth,

qPK = L + PvV, (26)

and that the sum of returns on business liabilities uses up the return tocapital,

ilL + ivPvV = ρqPK = rPK.

148 chapter four

Table 4.2 Balance sheets for an IS/LM model.

Households BusinessM Ω qPK LTh PvVPvV

Commercial Banks Central Bank GovernmentH M Tc H TL

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The symbols are il as the rate of interest on loans from banks (not thelong-term interest rate, as in section 5), iv as the rate of return to holdingequity, and ρ as the profit rate on the asset value of the capital stock (r isthe profit rate figured with respect to replacement value). The total re-turn to equity ivPvV follows as the return to capital minus interest costson loans.

If we let

λ = L/qPK, (27)

then combining the equations above gives an expression for q:

q = r/[λil + (1 − λ)iv]. (28)

That is, q is the ratio of the profit rate to a weighted average cost offinancing a unit of capital (a result less compelling than appears at firstglance since the weights themselves depend on q). Because ρq = r, it fol-lows that

ρ = λil + (1 − λ)iv.

The behavioral action subject to these accounting restrictions comesfrom the households’ asset demand balances. They are

v(iv, i, u)Ω − PvV = 0 (29)

τ(iv, i, u)Ω − Th = 0 (30)

µ(iv, i, u)Ω − M = 0. (31)

Equations (29)–(31) say that households spread their wealth overtheir three assets in the proportions ν, τ, and µ subject to the constraint ν+ τ + µ = 1.11 The demand proportions for shares, government bonds,and money are assumed principally to depend on the equity return iv, theT-bill interest rate i, and the output/capital ratio u respectively.

As already noted, these equations work in the same way as do excessfactor and commodity demand functions in a Walrasian system. In (29)–(31), rates of return and the price of equity adjust so that households ab-sorb predetermined stocks of assets. Specifically, for given u and Ω, iv

and i in (30) and (31) follow from the supplies of money M and T-billsTh. The equity price Pv is given by the demand function v(iv, i, u)Ω andthe supply of securities V in (29).

The last equations describe behavior of the banking system alonghighly traditional lines (analysis of asset and liability management on the

effective demand and its implications 149

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part of banks is deferred to Chapter 8). Money supply is determined as amultiple of commercial bank reserves:

M = ζH = ζTc. (32)

The corresponding supply of bank loans is

L = (ζ − 1)H. (33)

The multiplier ζ will typically be the inverse of a required reserve ratioimposed by the banking authorities. Loan supply follows in (33) fromthe commercial banks’ balance sheet identity.

The nine equations (25)–(33) determine nine variables: Ω, q, Pv, iv, il, i,λ, M, and L. Variables coming from outside this system include r, u, andP from the IS part of the economy; V, T, and K from historical accumula-tion processes; and Tc and Th from open market policy decisions.12

The implicit message of all this algebra is that the financial systemworks in myriad ways to balance claims among “agents” via movementsin appropriate rates of return. Modifying the model to avoid this mani-festly unreliable conclusion is a task left for later completion. For themoment, as far as money demand and supply are concerned, we cancombine (31) and (32) to get the relationship

µ(iv, i, u)[(qPK/T) + 1] − ζ(Tc/T) = 0. (34)

The Hicksian interpretation is that the money demand proportion µ isan inverse function of the bond interest rate i and (perhaps) the return toequity iv, and an increasing function of economic activity u. Demand forM is scaled by the expression (qPK/T) + 1, where the ratio qPK/T re-flects the breakdown of primary wealth between physical capital andgovernment liabilities. A higher value of capital relative to claims on thegovernment means that money demand rises, bidding up interest rates.On the other hand, an increase in the outstanding stock of governmentdebt T would reduce i, if the share Tc /T that is “monetized” is held con-stant.13

The overall money supply ζ(Tc /T) can be boosted by open market pur-chases to increase Tc or by an increase in the money/reserve ratio ζ.When ζ(Tc/T) goes up, the interest rate i has to fall to restore equilib-rium. If (34) is interpreted as an excess money demand equation with i asthe accommodating variable, then this adjustment is locally stable be-cause ∂µ/∂i < 0.

Figure 4.7 gives the standard picture, with (34) represented by the up-ward-sloping LM curve. As discussed in Chapter 8, the Pasinetti/post-Keynesian position is that the interest rate is determined prior to the real

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side of the system, so that LM has a shallow or horizontal slope.14 Themonetarist/Say’s Law story is a near-vertical LM. Hicks deserves creditfor coming up with a model which can capture such diametrically op-posed ways of looking at the world.

An IS curve to cross with the LM is already implicit in equation (9) inTable 4.1. We can leave out the distributional issues discussed at lengthin sections 1–3 by holding the profit share π constant. To look at fiscaleffects, it is convenient to bring in government spending (scaled by thecapital stock) γg as a demand injection. Putting equations in the table to-gether with the investment function (18) gives the condition that excessaggregate demand should be equal to zero:

γg + g0 + (απ + β)u − θi − [sππ + sw(1 − π)]u = 0. (35)

If the output/capital ratio rises when the left-hand side of this equa-tion is positive, short-term adjustment dynamics will be stable when thehigher u stimulates investment less than saving, as already observed inconnection with equation (14). If stability is assumed, excess aggregatedemand is an inverse function of both u and i, meaning that the two vari-ables trade off inversely to hold it equal to zero. The implication is thatthe IS curve slopes downward in Figure 4.7.

The standard thought experiment is to raise γg. IS shifts to the right,and both u and i increase. As the small arrows indicate, short-run ad-

effective demand and its implications 151

Interest ratei

Output/capitalratio u

S

I

L

M

Figure 4.7An IS/LM diagramwith a Hicksianliquidity trap.

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justment dynamics to such a shock in (34)–(35) are stable. Becausethe interest rate goes up (at least outside the liquidity trap/post-Keynesian/Minskyan flat LM curve case), capital formation may be par-tially crowded out.

These results are not dissimilar to those of the Wicksellian modelof Chapter 3, except that u replaces ¾ as the jump variable and Figure4.7 presupposes “fast” dynamics for i instead of its “slow” evolutionin Figure 3.5. The first change is by far the more important. It explainswhy between the Treatise and The General Theory Keynes became themost important economist of the twentieth century instead of remainingmerely a brilliant post-Wicksellian.

8. Maynard and Friends on Financial Markets

One of the joys of reading (and re-reading) The General Theory is tolearn from Keynes how “really existing” capital markets really function.They are a far cry from the smoothly adjusting rates of return in equa-tions (29)–(31), as illustrated with a couple of examples in this section.One shows how financial markets can help ratify macroeconomic equi-libria in which Say’s Law does not apply—they are a significant rea-son why capitalist economies may not be optimally self-adjusting.15 Theother demonstrates that insofar as capital markets generate sensible in-vestment decisions, they do so only because social arrangements pro-vide relatively stable background structures of expectations, prices, andcosts. The contrast with the perfect market-clearing, rational expecta-tions models set out in Chapter 6 is striking.

One source of instability and/or the persistence of socially undesirablemacroeconomic situations lies with the behavior of individual marketparticipants.16 Speaking from his own time and place, in Chapter 12 on“The State of Long-Term Expectation” Keynes described financial mar-kets as “beauty contests.” He was thinking not of Miss Great Britain butrather of 1930s competitions in English tabloid newspapers in whichreaders were asked to rank photos of young women in the order ofbeauty that they thought would be given by the average preferences of allother competing readers. The winning player would express not his orher own preferences, nor a guess at genuinely average preferences, butrather would reach “the third degree where we devote our intelligencesto anticipating what average opinion expects the average opinion to be.”In financial markets, professionals dig even deeper; “there are some, I be-lieve, who practice the fourth, fifth, and higher degrees” (p. 156).

There is no reason to expect a market—a financial market in particu-lar—operating on such principles either to make correct assessments

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about the “beauty” or somewhat more tangible attributes of corpora-tions such as their potential profitability, or to be stable against shocks:“A conventional valuation which is established as the outcome of themass psychology of a large number of ignorant individuals is liable tochange violently as a result of a sudden fluctuation of opinion due to fac-tors which do not really make much difference to the prospective yield,since there will be no strong roots of conviction to hold it steady. In ab-normal times, . . . the market will be subject to waves of optimistic andpessimistic sentiment, which are unreasoning and yet in a sense legiti-mate where no solid basis exists for a reasonable calculation” (p. 154).

Markets driven by average opinion about what average opinion willbe demonstrate two special behavioral patterns. As the quotation states,in “abnormal times” they can be volatile and prone to severe loss of li-quidity when all opinion shifts the same way. The liquidity squeeze candrive up the cost of capital, reduce investment, and slow growth in themedium run.

On the other hand, the prophecies of the market can be self-fulfilling:“We should not conclude from this that everything depends on waves ofirrational psychology. On the contrary, the state of long-term expecta-tions is often steady” (p. 162). Even so, such “equilibria” need not be so-cially desirable. Because it is shared by “a large number of ignorant indi-viduals” (be they highly paid Wall Street professionals or otherwise),market opinion crystallizes around Keynes’s “conventions,” often in theform of simple slogans.

Eatwell (1996) argues that beginning in the 1970s, for example, mar-ket opinion insisted on government “credibility” in terms of tight mon-etary policy and a “prudent” contractionary fiscal stance. If the author-ities did not comply by raising interest rates and cutting taxes and(especially) spending, the government’s bonds would be sold off, cuttingtheir prices and driving up interest rates anyway. In developed countries,at least, governments may have become prudent enough to accommo-date to pressures from volatile bond and foreign exchange markets, andby the late 1980s volatility had declined. But at the same time real inter-est rates trended upward (on the whole, real rates in the 1990s were athistorical highs with levels exceeding even those of the gold standard eraone hundred years earlier), growth outside the United States was notoutstanding, private firms cut back investment to levels consistent withslower output growth, and with reduced tax takes governments becameeven more fiscally constrained. And in developing economies after 1995,even extreme fiscal prudence could not ward off periodic financial crisesspurred by capital flight—abnormal times were not few and far between.

The notable exception to this interpretation was the very Keynesian

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“Goldilocks economy” in the United States in the late 1990s, when bothliquidity preference and private savings rates were very low and the out-put surge plus rising tax revenue (in part made up of healthy capitalgains taxes during the stock market boom) pushed the government intosurplus. How the rapid reversal of these tendencies at the end of the dec-ade (illustrated in Figures 1.1 and 1.2) will play out will only be knownin years to come.

Chapter 17 on “The Essential Properties of Interest and Money” inThe General Theory turns financial market stability on its head in an il-luminating way. A major implication is that price inertia in real andfinancial markets is essential to a capitalist system. Following Galbraithand Darity (1994) and Panico (1988), the basic ideas are the following.

One can imagine a durable asset—a house, say—which can be pur-chased for a price Pt

a this period or else at a price Pta+1(paid now) for de-

livery next period. Typically Pta+1 >Pt

a+1 so that there is a “spot premium”

(P Pta

ta/ +1 > 1) or “forward discount” (P Pt

ata

+1/ < 1) on the asset. Both andPt

a and Pta+1 are observed in the market, but the same is not true of an

expected price Pte+1 for spot sales next period. This price can be used to

define an “own-rate of return” ρ for the asset as17

ρ = [Pte+1 −Pt

a ]/Pta . (36)

Besides a return, an asset is also likely to have a carrying cost betweenperiods for storage, insurance, etc. On the other hand, if it can be soldrapidly for cash, it might also carry a liquidity premium (which would below or negative for assets such as half-constructed houses). Let c and lstand for carrying cost and liquidity premium respectively. Then theoverall return to owning the asset is ρ − c + l.

Fisher had already worked through the analytics of own-rates late inthe nineteenth century (Schefold 1997). Sraffa (1932a,b) picked them upin a polemic with von Hayek (1931). From a contemporary perspective,Hayek resembles an OLG theorist contemplating an economy on the“wrong” side of the golden rule. Along Austrian lines, he argued thatbusiness cycles result from excessive capital deepening and productionround-aboutness that occur because banks tend to hold the market inter-est rate below its “natural” level (for a formal example of such a cycle,see Chapter 9). Only a slump can undo the excessive capital formation.Moreover, attempts at expansionary policy during the downturn willjust make the underlying situation worse.

In opposition, Sraffa said that the short-term interest rate i is at best acenter of gravitation for the diverse own-rates of other assets. That is, for

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each commodity’s and capital good’s variables ρ, c, and l on the right-hand side, the relationship

i = ρ − c + l (37)

will only hold approximately. Out of full equilibrium there are myriadobserved own-rates. Even in equilibrium they will differ because theyrepresent diverse trends in relative prices, as Fisher realized and asPasinetti (1981) discusses at length. It is not possible to ascertain whatthe “natural” rate might be. No observable natural rate, no theory of thetrade cycle, and no justification for Hayek’s preferred contractionarymonetary stance (especially because he himself did not think it makesa lot of sense to compute averages of rates of return across differentsectors).

Ironically, Keynes to an extent argued along Hayek’s lines. He ob-served that if an investor is building up holdings of an asset, his or hercost of funds is i. With a stable or sluggish expected price Pt

e+1, more pur-

chases will tend to drive up the current asset price Pta until ρ from (36)

falls far enough to satisfy (37). At that point, the investor will stop buy-ing. In other words, there are market forces driving ρ − c + l toward thevalue i, although they may not complete the task in any short period oftime.

Now suppose that i declines. A buying process will begin, driving upPt

a. As the expected return to acquiring the asset today begins to drop offfrom (36), it becomes more appealing to buy forward. But then Pt

a+1 will

also increase, because spot and forward prices of producible assets tendto move together. This co-movement is in fact what triggers capital for-mation. To see why, we have to bring in another price Pt

c, or the “costprice” of manufacturing the asset. When P Pt

atc

+1 / , entering into produc-tion for forward sale becomes an appealing option.

This Sraffa/Keynes theory of investment demand is deeper than thestandard MEC chronicle. Several observations are worth making. Thefirst is that the decision-making process just described relies on stabilityof the expected price Pt

e+1 and the cost price Pt

c. Suppose that Pta+1 moves

in proportion to Pta (the spot premium is stable) and that Pt

e+1 moves in

proportion to Pta+1. Then the investment increase just described can never

happen. An initial rise in Pta will be matched proportionately by a higher

Pte+1 and from (36) a reduction in ρ cannot occur (ultimately the interest

rate would have to rise back up to meet ρ, as in the steady state ofRamsey growth models). Similarly, if the cost price Pt

c jumps up whenPt

a+1 does, no one can make a profit by producing more of the asset.

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This latter observation shows that nominal cost anchors are an essen-tial attribute of capitalist accumulation. Investment can not take placeunless costs (and in particular wage costs) are relatively stable. Similarly,the current economic situation cannot move unless changes in expecta-tions are sluggish. Stated differently, we have just proved a “policy inef-fectiveness” proposition: even if investment is very low, reducing the in-terest rate will not stimulate more capital formation when Pt

e+1 and Pt

c

rapidly adjust to the lower level of i. In the context we are considering,postulating such speedy price adjustment looks a little bit crazy; after all,the economy does accumulate as it moves from one configuration to an-other in historical time.

Contrariwise, if one believes that the current configuration is “opti-mal” in some sense, then rapidly adjusting or “rational” expectationsbecome a powerful rhetorical weapon—we’re in the best of all possibleworlds and speedy adjustment of expectations will keep us there. Subse-quent chapters describe how aggressively new classical economists havesold this line.

Finally, the more relatively stable are prices such as Pte+1 and Pt

c, themore important are likely to be quantity shifts in mediating macroeco-nomic adjustments (a point already raised in the context of the Ramseymodel in Chapter 3). But what stabilizes asset prices and rates of return?In an unjustly neglected pair of papers written in the late 1930s, Kaldor(1960a,b) built on Keynes by demonstrating that speculators in the bondmarket can do the job of stabilizing the own-rate structure with theshort-term interest rate set by the central bank as the anchor, unless ex-pected asset and commodity prices are highly elastic to changes in cur-rent conditions. Among the own-rates will be profit rates in production.Closing a great circle, Kaldor’s work supports Sraffa’s (1960) suggestion(mentioned in Chapter 2) that the money rate of interest regulates the in-come distribution along the wage-profit frontier.

If expected prices are sensitive to changes in the current situation, thenspeculation can be destabilizing, with the losses of many unsuccessfulspeculators keeping the profits of a successful few quite healthy. Kaldordid not presume the existence of super-rational representative agents,and failed to see the possibility of a perfect foresight interest rate and as-set price saddlepaths as discussed in sections 5 and 9. Perhaps that wasbecause he thought he was theorizing about the real world.18

9. Financial Markets and Investment

The foregoing discussion leads naturally to consideration of other fac-tors that may influence the investment decision. In this section, we take

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up two approaches—the first post-Keynesian19 as propounded by peoplelike Minsky (1986) and the second based on Tobin’s q.

It is clear from the own-rate models just discussed that the investmentdecision hinges on comparing the asset price Pa with the cost price Pc ofthe bundle of capital goods under consideration. An immediate compli-cation is that the enterprise making the comparison can draw on threedisparate sources of finance: liquid assets on hand; the enterprise’s cur-rent flow of gross profits after payment of existing debt service and inter-est obligations, dividends on equity, taxes, and expenditures for “busi-ness style”; and finally external funds to be obtained by issuing newliabilities. These sources of funding carry different costs and obligationswhich fundamentally influence investment decisions. Enterprises operatein highly imperfect capital markets; they do not live in a Modigliani-Miller world.

For firms apart from Microsoft in its glory days, liquid assets are notgoing to be substantial.20 Moreover, as already noted in Chapter 1, theirdesired investment may well exceed retained gross earnings on a contin-uing basis so that external funds are required. In American practice,firms will often initially finance a project by borrowing from banks orthe money market, and then refinance with longer-term obligations.21

Figure 4.8 illustrates the complications.The schedule for the “Internal funds limit” on investment is a rectan-

gular hyperbola: PcI = F, where I is the volume of investment, Pc isits cost price, and F is the available flow of internal funds. The cost price

effective demand and its implications 157

Assetprices

Investment

A

Lender’s risk

Internal funds limit

Borrower’s risk

Pa

Pc

Figure 4.8Post-Keynesianinvestment theory.

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begins to rise for levels of investment lying to the right of this curve.There are several reasons why. Supply costs may begin to go up as cap-ital goods producers begin to hit capacity limits. Meanwhile, “lender’srisk” becomes increasingly important.22 As a firm borrows more from itsbanks, they are likely to raise interest rates, shorten loan maturities, andattach “covenants and codicils” to loan agreements to force the bor-rower to restrict current dividends, restrain further borrowing, not sellassets, and even keep a floor under business net worth. Higher interestrates do not give a full picture of rising financial costs, which is why the“Lender’s risk” curve is drawn with dashes.

“Borrower’s risk” also goes up with the volume of investment. Toquote Minsky (1986) directly, the investing firm either has “to run downholdings of financial assets that are superfluous to operations, or to en-gage in external finance. If financial assets are run down, then margins ofsafety in the asset structure are reduced. If new issues of common sharesare undertaken, the issue price will have to be attractive, which maymean the present stock owners will feel their equity interest is being di-luted. If debts, bonds, or borrowing from banks or short-term marketsare used, then future cash-flow commitments rise, which diminishes themargin of safety of management and of equity owners. . . . [B]orrower’srisk will increase as the weight of external or liquidity diminishing fi-nancing increases. This borrower’s risk is not reflected in any objectivecost, but it reduces the demand price of capital assets” (pp. 191–192).

In diagrammatic form, Pa drops off for high levels of investment, asshown by the dashed “Borrower’s risk” schedule. There is a notional“equilibrium” at point A, which determines the level of investment ac-tually undertaken. Typically, A will lie to the left of a neoclassical in-vestment equilibrium just because lender’s and borrower’s risk restraincapital formation. These schedules as drawn may also shift for severalreasons.

First, a less severe internal funds restriction (represented by a right-ward shift of that schedule) would push both the dashed schedules to theright, stimulating capital formation.

Second, by pulling down own-rates of return as discussed above,lower short-term interest rates will push the asset price Pa upward. Be-cause as discussed in Chapter 3 interest rates enter into production costs(especially for investment projects with long periods to maturity), theirreduction will move the cost price Pc downward. Both shifts will movethe intersection point A to the right. The resulting inverse relationshipbetween the interest rate and new capital formation reflects not just “de-creasing returns to capital,” but rather the financial and institutional ad-justments that permit more rapid accumulation to take place.

Third, when this environment changes, so will investment behavior. A

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boom will increase corporate profits and shift the Internal funds limitcurve to the right, reducing the rate of increase of lender’s risk. It is alsolikely to shift Pa up. We get an “accelerator” investment response, butagain one dependent on institutions.

Finally, if we return to Keynes’s beauty contest, attitudes of financialmarket actors affect the slopes of the Lender’s and Borrower’s risk sched-ules. They may change configurations suddenly, or stay locked in placefor extended periods of time. If the dashed curves in Figure 4.8 are steepand at the same time internal funding possibilities are low, there is scantreason to expect high investment and a socially desirable rate of eco-nomic growth.

These downside “uncertainties” (in Frank Knight’s terminology) areblissfully ignored in recent mainstream investment theories. Their focusis on the dynamics of capital formation resulting from postulated opti-mizing behavior of firms facing perfect capital markets. The paradig-matic q-model was presented in section 5 of Chapter 3, and we exploreits dynamic properties here.

Restating the relevant Euler equations for convenience, we have an ac-cumulation rule for the growth of a firm’s capital-labor ratio k,

| = gk, (38)

where g is the growth rate. There is an asset price q corresponding to k,and g is optimally determined by the formula

q = 1 + h(g) + gh′(g), (39)

where gkh(g) is an “installation” or “shut-down” cost associated withthe change | of the capital/labor ratio caused by a nonzero value ofthe control variable g (which can be either positive or negative). In-verting the expression on the right in (39) makes g an increasing functionof q, and the properties of the cost factor h can be cunningly chosen tomake the value q = 1 correspond to a steady-state growth path alongwhich g = |/k = 0.

Finally, there is an optimizing rule for the growth of q. It can be statedin two ways,

i = [f′(k) + g2h′(g)]/q + É/q (40a)

or

É = iq − [f′(k) + g2h′(g)]. (40b)

At an initial steady state with É = g = 0, (40a) reduces to i = f′(k)/q.Taking into account the transition from discrete to continuous time, thisformula amounts to a combination of Keynes’s equations (36) and (37)

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tying an asset’s own rate of return ρ to the interest rate i (ignoring the li-quidity premium l and carrying cost c), with the own-rate in the presentcase being ρ = f′(k)/q.

Now let the interest rate shift downward. As discussed above, theown-rate must also jump down via an increase in the asset price q. Be-cause g is an increasing function of q from (39)—this is the “q” theory ofinvestment demand—| will be positive from (34). The positive value of gwill also make É < 0 in (40b), even though iq − f′(k) = 0 in the “in-stant” that the interest rate moves. To summarize, the asset price jumpsupward when the interest rate is cut, inducing investment demand and agradual reduction of the price itself.

This process looks vaguely under control, except for the iq term on theright of equation (40b). As in the previous perfect foresight models thatwe have encountered, this term sets up a positive feedback loop in whicha reduction in q makes É < 0 and reduces q further still. What factorscan make this cascade of capital losses (negative own-rates of money re-turn in Keynesian jargon) come to a halt? There are two possibilities.One is to postulate that expectational dynamics for asset prices are a lotmore sluggish than those built into (40b) for q. To a degree, this solutionwas adopted by Kaldor (1960a).

The other ploy is to stick with (40b) because it has MIRA foundations,and push rationality to the hilt. As illustrated in Figure 4.9, the system(38)–(40) has saddlepoint dynamics. A lower interest rate shifts the locus

160 chapter four

Assetprice

q

Capital/laborratio k

A

C

SB

S

k = 0

q = 0

q =1

.

.

Figure 4.9Saddlepoint dynam-ics for capital ac-cumulation whenthe interest rate isreduced.

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along which É = 0 upward, setting up a saddlepath SS. The asset pricejumps from its initial steady-state level of unity at A to a higher value atB on the new saddlepath, and begins a gradual decline to a new steadystate at C. Capital accumulation | also initially jumps up and then grad-ually slows back to zero.

Appropriate transversality conditions on q and k can make this pro-cess work out, avoiding dynamic trajectories along which q goes toinfinity or zero (Blanchard and Fischer 1989; Romer 2001).23 One ques-tion is whether the capitalist enterprises one reads about in the WallStreet Journal and Financial Times have the market agility required toleap to and remain in balance along the saddlepath. One can perhaps bepermitted a modicum of doubt.

Second, even if the Figure 4.9 capital formation path were to workout, it lacks verisimilitude. As any reader of Keynes and Minsky is wellaware, investment dynamics in any observable market economy are farricher than the story just recounted. Interest rate reductions do not justcause investment immediately to jump up and then gradually die off—repercussions within the firm and on both the real and the financial sidesof the economy bring much more oscillatory accumulation processesinto action. Some are discussed in Chapter 9.

10. Consumption and Saving

If investment is at the heart of the injection side of the Keynesian calcu-lus, then saving has equivalent importance as a leakage. In Anglo-Ameri-can financial structures, at least, the biggest shares of gross national sav-ing are provided by businesses and by households in the top few percentof the size distribution of income. One might expect that the bulk of re-search would be on the generation and allocation of corporate and highpersonal income flows. Most professional attention, however, has con-centrated on average saving rates. In part this emphasis follows TheGeneral Theory itself, but it also reflects mainstream perceptions. If theModigliani-Miller theorem means that finance is a veil, then it makessense to concentrate on households as the ultimate savers. And the repre-sentative agent hypothesis makes all households look the same.

In the beginning, Keynes himself thought that the overall marginalpropensity to consume dC/dY (where in The General Theory Y standsfor an income concept resembling real GDP) would be less than the aver-age propensity C/Y. Keynes did not write out an explicit equation for hisconsumption function C(Y), but the literature soon came to accept a lin-ear version

C = a + mY (41)

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(with a and m both positive and m < 1). Keynes went so far as to termthe m < 1 condition a “fundamental psychological law” (p. 96). Poppsychology from a genius, alas, turned out to be no more reliable thansimilar pronouncements from less august sources.

Problems showed up within a decade of The General Theory. One wasthat even though real disposable income in the United States fell between1945 and 1947, there was no postwar consumption slump (as had beengenerally predicted). Spending from wealth in forms such as savingsbonds built up during the war and a general recuperation from the na-tional vicissitudes beginning in 1929 provided ad hoc explanations, butleft the “psychological law” suspect.

Analysis of time-series data by Kuznets (1946) and others also posedproblems. The marginal propensity to consume appeared to varycountercyclically, falling in booms and rising in slumps (a possibility al-ready recognized by Keynes, who had access to Kuznets’s preliminaryempirical results). Over longer time spans, a companion finding was thatthe intercept term a in (41) tended toward zero. The reason is easy to seeif we consolidate household accounts for income and expenditure, flowsof funds, and change in wealth:

Y − C = S = ô,

where Y now represents real household income, S is household savingand ô is the increment in household wealth (all variables are figured percapita). In a steady state or over a long period of averaged data, let thegrowth rate of Ω be g. Then manipulation of the accounting statementabove gives

C/Y = 1 − (Ω/Y)g. (42)

For g amounting to a few percentage points and Ω/Y in the range ofone to three, C will be around 90–95 percent of Y. This theorem of ac-counting underlies a diagram like Figure 4.10, where the “Keynes” con-sumption function crosses a long-run relationship like (42). Over peri-ods of quarters or a few years, data points may (or may not) clusteralong the Keynes relationship, but the schedule itself cannot be stable. Inan economy with real per capita income growth it has to shift upwardover time to permit the average ratio C/Y to satisfy (42).

Beginning in the 1940s, an active cottage industry grew up attemptingto explain these findings. Here we sketch three early approaches in in-creasing order of influence on the mainstream (and decreasing order ofinstitutional interest). The first was advanced by Duesenberry (1949).One basic idea was that each household’s consumption behavior is the

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result of learning, custom, and habit (points already made in The Gen-eral Theory). People do watch each other as well as the movies and TV,and shape the level and composition of their spending accordingly.

Second, consumption is somewhat inertial. When Y swings up, C risesbut with a lower rate of growth. When Y declines, households try to re-tain existing real standards of living, so that C drops off with a lag. Informal terms, Duesenberry argued that C is likely to depend on pastpeak real income as well as current Y, giving rise to a “ratchet effect.” Inan upswing, C moves along a “Keynes” curve in Figure 4.10, but itdoesn’t fall very much when Y declines. Thus in the next upswing the in-tercept of the “Keynes” schedule has risen, providing a mechanism forits drift upward over time.

Duesenberry’s model explained the stylized facts of its time (the highconsumption level after World War II, the countercyclical marginal pro-pensity to consume, and equation (42)) parsimoniously and with a bit offlair. It would be interesting to see how well it would apply to the periodof stagnant household income (but rising income inequality) betweenaround 1970 and the late 1990s. But such studies have not been made.Although it sounds sensible, the ratchet effect lacks MIRA foundations,and consequently vanished from professional view.

The “life cycle” consumption model of Modigliani and Brumberg(1954) and Ando and Modigliani (1963) took a step from Duesenberrytoward MIRA fundamentals, but at least tried to describe the ways inwhich people plan their economic lives. The households considered,

effective demand and its implications 163

ConsumptionC

Income Y

Long run

Keynes

45°

Figure 4.10Alternative consump-tion functions.

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however, are of a certain age and kind. As Marglin (1984) observes,“People whose employment prospects are reasonably certain, who fol-low a reasonably predictable career path, and whose lives are other-wise sufficiently ordered that long-term planning makes intellectual andemotional sense might . . . make decisions according to the life-cycle hy-pothesis . . . (A colleague of mine once remarked that the life-cycle hy-pothesis is just what one would expect of a tenured college professor!)”(p. 431).24

Such a well-ordered person might be T years old, expecting to live toage L and to work to age N. Let ω be expected yearly average wage in-come for the rest of his or her working life. Then his or her consumptionfunction at age T could take the form

CT =Ω+ −

ω( )N TL T

, (43)

where it is understood that the term ω(N − T) drops out when the per-son retires (that is, ω = 0 when T > N). Somebody aged forty-five whoexpects to work to sixty-five and die at seventy-five will thus consume3.33 percent of his or her wealth per year and 66.67 percent of expectedaverage wage income. Evidently these coefficients will change over a per-son’s life cycle, but the population-wide numbers add up to somethinglike the Keynesian consumption function (41).

Except for those who are about to die, the consumption coefficient onwealth in this setup is pretty small—a few percent per year for the mid-dle-aged and near zero for the young. Such models correctly predictedthat the paper losses of one or two trillion dollars in the stock marketcrash of October 19, 1987, would not be large enough to cause a reces-sion in 1988. (As of this writing, what will happen as a result of drop-ping asset prices in 2001–2003 remains to be seen.) Life-cycle consider-ations also suggest that the real balance effect is of extremely limitedsignificance for consumption behavior, because in the United States total“liquid assets” (currency and deposits, money market funds, and cashsurrender value of insurance and pension accounts) amount to less than20 percent of household wealth (Wolff 1995). This observation is ig-nored by the mainstream.

There are other problems with the life-cycle model. The version in (43)includes no “bequest” motive for a person to die with Ω> 0 so as to en-sure the livelihoods of her or his heirs, although that could easily beadded. More fundamentally, to quote from Marglin (1984) again, thegroup to whom the Modigliani et al. hypothesis applies

is hardly representative of the population as a whole—neither of thetop 1 or 2 percent of the income distribution who account for a dispro-

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portionate amount of total saving and for whom other motives thanprovision for retirement appear to be significant, nor of the bottom 80to 90 percent of the distribution who account for most savers, if not formost saving. . . . [Their prospects] are so uncertain that deliberatechoice and planning are beside the point. . . . The life-cycle hypothesismay adequately account for the . . . professionals and executives whosefutures are sufficiently secure to make deliberate provision for the fu-ture a reasonable notion and whose relative means make the pressureto spend less imperative. . . . This leaves us with the upper end of the in-come distribution, not just the super-rich but the top 1 to 2 percent . . .candor compels the admission that we know very little about the savingbehavior of the people who do most of the saving. (p. 432)

With regard to the super-rich, moreover, standard theory fails to ex-plain why anyone would want to build up a huge fortune in the firstplace—after the first few hundred million dollars, providing consump-tion possibilities for oneself and one’s heirs must cease to be a con-cern. Desires for power and prestige along with the thrill of playing themoney-making game are obvious motivations, but they don’t fit wellinto most economists’ models.

More on Marglin’s ideas about saving behavior below, but next wehave to discuss the most influential mainstream theory—Milton Fried-man’s (1957) permanent income hypothesis (PIH). The simplest ratio-nale is provided by someone with a known, finite lifespan and an incomestream that fluctuates over time. This person is assumed to have access toa perfect capital market, and can borrow or lend at a zero interest rate.What plan will maximize the integral of his or her consumption “felic-ity” (or utility from consumption at each point in time)?

The answer is that consumption per unit time will be a constant equalto the sum of the person’s expected lifelong income flows divided by thelength of his or her life. The reason for this is that any blip upward froma level consumption path would have to be matched by an equal blipdownward at some other time to satisfy the lifetime budget constraint.But with diminishing marginal utility of consumption, the “utils” gainedin the upward blip are less than those lost from the one going down. Theimplication is that all blips (let alone trends or more complicated fluctua-tions) will be avoided.

Such a person’s consumption would be unaffected by “transitory” in-come fluctuations above or below his or her lifelong average (or “perma-nent”) level and would satisfy (42) with saving varying procyclically. Wehave another explanation for the post–World War II stylized facts—onethat makes the marginal propensity to consume out of current incomevanishingly small.

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This last observation explains why the PIH was an important earlysalvo in the orthodox attack on the Keynesian edifice. If the marginalpropensity to consume out of current income is near zero (or the mar-ginal propensity to save is near one) then injection/leakage and multi-plier calculations fall apart. A “temporary” tax change such as LyndonJohnson’s surcharge of 1968 will not reduce consumer spending, as infact it did not appear to do. A “permanent” change such Ronald Rea-gan’s tax reduction of 1982 might be expected to have more bite, as“verified” by the boom that followed.

Such macroeconomic correlations can be explained in a thousandways, of course, which is why one has to ask about the nature of the the-ories underlying the explanations. The PIH is attractive to the main-stream because of its optimizing foundations. The maximizing problemstated above is a special case of the Ramsey optimal saving model, inwhich both the return to alternative uses of funds (or the profit rate) rand the person’s pure rate of time preference j are set equal to zero. Re-call from equation (20) of Chapter 3 that consumption behavior in thegeneral case is described by the Ramsey-Keynes rule

ƒ = (C/η)(r − j), (44)

where η is the elasticity of the marginal utility of consumption (and 1/η isthe intertemporal elasticity of substitution in consumption). We have ƒ= 0 when r → 0 and j → 0, or Friedman’s result.

Relationships like (44) have generated enormous academic churning,due in part to the post-PIH mainstream fashion of basing consumptiontheory on Ramsey-type models solved under the assumption that com-plete probability distributions can be put on future household incomeflows, including returns to assets. For the reasons mentioned above inconnection with the liquidity preference and investment functions, thisapproach is strikingly anti-Keynesian.

With regard to asset valuations in particular, Keynes thought that “theexisting market valuation [of an asset] . . . cannot be uniquely correct,since our existing knowledge cannot provide a sufficient basis for a cal-culated mathematical expectation” (p. 152). He continued: “Human de-cisions affecting the future, whether personal, political, or economic,cannot depend on strict mathematical expectation, since the basis formaking such calculations does not exist; and it is our innate urge to ac-tivity which makes the wheels go round, our rational selves choosing be-tween the alternatives as best we are able, calculating where we can, butoften falling back for our motive on whim or sentiment or chance”(pp. 162–163).

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Details about how to ignore Keynes and solve Ramsey models underquantifiable risk using stochastic dynamic programming are postponeduntil Chapter 6. For the moment, we can briefly mention three topicsthat have been hotly debated in the literature before going on to more in-teresting material—the random walk hypothesis, interest rate effects onsaving, and the puzzle of the equity premium.

The random walk model shows up if we set r = j = 0 in (44) but com-pensate by throwing in a random error term À on the right-hand side,

ƒ = À. (45)

It is straightforward to show that (45) will be an optimal decision rulefor the Friedman problem described above when felicity takes the formof a quadratic function and income per unit of time is subject to a ran-dom shock (again assumed to be described by a calculable and completeprobability distribution as opposed to being “uncertain” à la Keynes andKnight).25

The significance of equations like (45) as “tests” of the PIH and simi-lar optimizing formulations was pointed out by Hall (1978), who pro-vided econometric support for the hypothesis that period-on-periodchanges in consumption are an uncorrelated random process, that is,a random walk. Countless econometric exercises later, the mainstreamconsensus seems to be that despite the attractiveness of (45), both thelevel and the change in C are affected by permanent and transitory fac-tors, in Friedman’s terminology (Romer 2001). We come down not toofar from Keynes’s model of consumption.

The potential effects of interest rate changes on consumption are mosteasily contemplated in a Fisher diagram like the one in Figure 3.1. Ahigher interest rate rotates the corresponding schedule clockwise, givinga real income loss “today” (presumably reducing saving) and inducing ashift along an indifference curve toward more consumption “tomor-row” (and thereby saving “today”). If real wealth goes up because of alower interest rate, saving will presumably fall. Which effect will domi-nate is not immediately clear. The ambiguous diagram aside, casual ob-servation suggests that people don’t adjust their saving much in responseto interest rate changes. In a Ramsey model framework, however, Sum-mers (1981) tried very hard to argue the opposite case. In the notation of(44), he thought about a long-lived individual for whom r is slightly big-ger than j and 1/η is small. The growth rate of consumption is thusslightly positive, meaning that the level of C at a long life’s end will benoticeably bigger than at its beginning.

To satisfy this plan, the individual will have to save a lot in his or her

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early years, put the money into assets with a return r, and then dis-savemassively toward the end along the lines of the life-cycle equation (43).This particular pattern of behavior will be quite sensitive to changes in r.Summers makes a good lunge at forcing saving at the aggregate level tobe interest rate–sensitive, but in light of Marglin’s observations above, hedoesn’t get the ring. To repeat, just how many people in the populationare in a position to make such precise calculations, and what proportionof total saving do they provide?

Finally, the “puzzle of the equity premium” refers to Mehra andPrescott’s (1985) observation that the average long-term return to hold-ing stocks in the U.S. economy is about 7–8 percent while the “riskless”real return on Treasury bills is about 1–2 percent. The “puzzle” emergesfrom the following line of reasoning in a standard finance theory modelin which asset-holders maximize expected consumption under calculablerisk (Kocherlakota 1996)—the capital-asset pricing model (CAPM) isthe standard story.

If the covariance of an asset’s return with its holder’s consumptiongrowth is high, then it makes sense for the holder to sell that asset andbuy another one with a low (or, better, negative) covariance—in thatway overall variance of consumption is reduced. To induce the holder tokeep the high covariance asset in his or her portfolio, then, those hold-ings have to pay a high return. The puzzle is that in the United States thecovariance of equity returns and consumption growth is well less than0.005 while the differential in rates of return between T-bills and equityis 0.06. If holding equity poses such a tiny covariance risk, why is its re-turn so much higher than that on bonds?

Mainstream economists have no clear explanation for the differencein returns. They mumble about transactions costs in the stock market,but sound unconvinced. Readers of Keynes could respond that these ob-servers’ perception of how the market functions is not correct. Its drivingparticipants are not households interested in maximizing expected utilityfrom consumption, but rather professionals competing against one an-other in search of high short-term returns, probing market opinion to“the fourth, fifth, and higher degrees.”

In such a game among insiders, the carrying and illiquidity costs oftaking positions are important matters; in terms of equation (37) theown-rate of return to holding shares must be correspondingly high.Nifty little formalizations may now (and forever) be lacking, but it ishard to see how this Keynesian institutional explanation of the elevatedreturn to equity as a compensation for speculation’s Knightian “uncer-tainty” could be badly wrong. Its active players segment the stock mar-

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ket away from the rest of the economy in which passive investors arehappy to get a good rate of return; within the market’s own precincts,the stakes are very high.

11. “Disequilibrium” Macroeconomics

To end a survey of Keynesian economics, one last debate about short-term adjustment is of interest. The key issue can be illustrated by thesharp distinction between two theories of consumption demand dis-cussed in the last section. One is Keynes’s “fundamental psychologicallaw” stating that current real consumption is mainly a function of cur-rent real income. In other words, consuming households are constrainedin their decision making by whatever money happens to be coming in.On the basis of rules of thumb, slow adjustment to income fluctuations,and maybe a little bit of saving for a rainy day, at time t they basicallyscale C(t) to the amount of income Y(t) that is available.

Friedman’s permanent income hypothesis, on the other hand, says thathouseholds have a present and future “endowment” of income flowsthat they can foresee pretty accurately. With access to a (nearly) per-fect capital market they can borrow and lend to smooth away incomefluctuations and keep a stable consumption path. The only income (orwealth) constraints they face are their fixed lifetime endowments. Thisview is Walrasian in that it presumes that prices will adjust smoothly togenerate full employment income flows over time. Households plug thisinformation into their dynamic optimizing programs, and buy accord-ingly.

Three decades after The General Theory, Clower (1965) stirred upwaves by pointing out that Keynes did not think like Friedman orWalras. Clower propounded a “dual decision hypothesis.” In onechoice, households base consumption expenditure on the current incomethey receive, which depends on the overall level of employment. In theother decision, firms choose employment levels based on their currentvolume of sales. Such decision procedures boil down to an injections/leakages calculus, not a Walrasian scenario in which prices rapidly ad-just to ratify full employment levels of incomes and sales.

Building on Clower, Leijonhufvud (1968) soon added that expectedprices and wages are likely to respond sluggishly to changing events andthat “perverse” responses to macroeconomic dislocations can be ex-pected.26 All this could not have been surprising to anyone who hadtaken The General Theory (as opposed to Patinkin-based and IS/LMglosses) to heart. The Clower-Leijonhufvud tempest blew itself up be-

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cause by the mid-1960s in (especially) the United States and the UnitedKingdom authentic Keynesians were a rare breed; neoclassical synthesiz-ers were in full cry.

In Europe, on the other hand, Malinvaud (1977) took the dual deci-sion line a step or two further, drawing on his experience working withthe French “indicative” planning bureaucracy in the 1950s and 1960s. Afrequent argument between the labor unions and the bureaucrats con-cerned the effects of an increase in the real wage—would it add to em-ployment by raising aggregate demand, or reduce it by driving up laborcosts? Malinvaud’s answer took the form of a variation on Figures 4.2and 4.3.

The gist is illustrated by the “arrowhead diagram” of Figure 4.11,in which aggregate demand is assumed to be wage-led along the posi-tively sloped schedule. Firms will only employ more workers, on theother hand, when the real wage falls along the “Labor demand” curve.Malinvaud’s innovation was to assume that employment is determinedby a “short-side rule” operating across the commodity and labor mar-kets. For example, if the real wage is low, then aggregate demand alongits schedule will be less than the output firms would be willing to pro-duce with cheap labor. Output and employment will be limited by de-mand on the “short” side of the market, in a situation of “Keynesian un-employment.”

Alternatively, for a high real wage, desired commodity demand will

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Real wageω

Output/capitalratio u

Classicalunemployment

Keynesianunemployment

Aggregatedemand

Labor demand

u

Figure 4.11Malinvaud’s arrow-head.

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exceed the quantity firms are willing to provide. “Classical unemploy-ment” along the labor demand curve will be in force. Given the level ofthe real wage, the economy will find itself somewhere on the darkenedsegments of the curves. The model generalizes The General Theory inso-far as Keynes operated at the point of the arrowhead where both sched-ules are in force.27

As discussed above, Keynes thought that higher aggregate demand(dashed line) would be associated with higher output and a lower realwage. With the model closure of Figure 4.11, this conclusion is modifieddepending on the level of the real wage ω. If ω is low, higher demand willraise output at a constant wage. If ω is high, expansionary policy simplywill not work. In both cases, if at a given ω the aggregate demand locuscrosses the “full employment” activity level Ä, then an intuitively ob-scure “repressed inflation” equilibrium will kick in.

Just listing all these cases suggests why disequilibrium macroeconom-ics did not take hold. Malinvaud and colleagues such as Benassy (1986)took the nonlinear MIRA mathematics (not to mention econometrics)underlying Figure 4.11 quite seriously. By the time they had writtendown all the switching rules among regimes in formal terms, the equa-tions were intractable and ugly. A more flexible, institutionally basedanalysis of the adjustment possibilities implicit in the diagram mighthave proved enlightening. But because they were locked into their “non-Walrasian” MIRA way of thinking, qualitative, history-based analysiswas not within the reach of the best Continental economists of the1970s.

12. A Structuralist Synopsis

The foregoing arguments have been lengthy and convoluted. It makessense to step back and review the major macroeconomic points. Follow-ing Gordon’s (1997) econometric summary, they include the following.

Investment demand does appear to respond positively to the profitrate r and capacity utilization u, and negatively to the interest rate i. Thestandard econometric tests suggest that savings flows do not “cause” in-vestment either by being important right-hand-side variables in regres-sion equations or by chronologically “leading” capital formation.

Aggregate consumption responds positively to u and negatively toprofit income flows, consistent with different propensities to consumefrom wage and nonwage income. Consumption and saving react weakly,if at all, to changes in the interest rate, but do appear to have a strong in-ertial component à la Duesenberry. Marglin’s (1984) “disequilibrium hy-pothesis” via which household “saving occurs when income rises faster

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than households can adopt their spending habits; dissaving occurs whenincome falls faster than households can rein in their spending” (p. 145)appears to fit the data reasonably well.

The essentials of the principle of effective demand thus appear to havesurvived sixty years of intense scrutiny. Moreover, strong attacks to agreater or lesser extent have misfired.

First, even impeccably mainstream economists such as Carroll andSummers (1991) reject the permanent income hypothesis by admittingthat consumption growth tracks income growth, and that savings ratesdiffer across income classes. One reason is that households with scantwealth are recognized to be subject to “liquidity constraints,” and con-sume according to “rules of thumb” as opposed to optimizing scenarios(Shefrin and Thaler 1988).

Second, anomalies such as the “equity premium puzzle” suggest thatall is not well with the axiom that financial markets perform perfectly.The views of Keynes and colleagues on the significance of essential un-certainty, financial “beauty contests,” and institutional structures havenot been overturned. The implication is that idealized models of invest-ment and saving along Ramsey’s lines are far removed from macroeco-nomic reality.

Third, as argued more fully in following chapters, Say’s Law is nottrue—saving does not drive investment and full utilization of labor andinstalled capacity are not observed.

Effective demand remains the valid approach to macroeconomics. Thequestion is how to use it to understand and improve the social impacts ofthe existing macroeconomic system.

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chapter five

z

Short-Term Model Closureand Long-Term Growth

Effective demand may be alive and kicking, but it is under intense com-petition from macroeconomic theories with opposing ethical and episte-mological foundations. The alternatives are considered together in thischapter, in a journey over once-trod ground with some new attractionsthrown in. The goals are to take a breather after racing through a lot ofdifferent models, and to set the stage for further analysis.

We begin by summarizing how the models we have discussed behavein the short run (concentrating on the real as opposed to the financialside of the economy), and go on to consider their extension into theoriesof growth rooted at least partly on the supply side—Solow, Kaldor, andMarxist formulations. The next section focuses on the demand side, cov-ering stability or lack of same in Harrod-style growth models. We closewith an introduction to a demand-driven model used extensively in laterchapters. It is used to analyze pension programs as was done with theOLG model in Chapter 3. The supply- and demand-driven formulationscome to virtually opposite conclusions about the macro effects of pay-goand fully funded social security programs.

1. Model “Closures” in the Short Run

Two fundamental points are that the accounts in the SAM underlying aone-sector macro model plus a small number of additional “behavioral”assumptions serve completely to determine the model’s properties, andthat these properties can differ strikingly depending on just which be-havioral relationships are imposed.

Although they are implicit in Keynes’s transition from his forced-sav-ing Treatise to the output-adjusting General Theory, explicit statementsof these ideas emerged only after his death from his immediate disciplesin Cambridge, for example, Robinson (1956) with her various “ages” ofgrowth and Kaldor (1956) on alternative theories of distribution. Theywere picked up by Sen (1963), Harris (1978), Taylor and Lysy (1979),

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Marglin (1984), and Dutt (1990). Taylor and Lysy (1979) popularizedthe not overly felicitous word “closure” as a shorthand description of amodel’s causal structure.

Table 5.1 sets the stage for closure analysis in an economy withoutforeign trade and in which monetary linkages are ignored (for the mo-ment). It follows along the lines of Table 4.1 in presenting two similarbut not identical macro models—the one to the right with neoclassicalassumptions about uses of inputs and income distribution is more inter-nally constrained or closed than the one to the left with markup pricing.The causal structure of both versions rests on determination of price andinput-output relationships from equations (1)–(4), and the level of de-mand from (4)–(7). How the two sets of equations interact is determinedby a handful of additional restrictions. We can quickly run through casesthat appear in the literature—models characterized by output adjust-ment, forced saving, loanable funds, IS/LM, real balance effects, infla-tion effects, determination of investment by saving supply, and closureby adding extra variables.

Output Adjustment

In the markup model, assume that the nominal wage w is fixed byhistorical wage bargains and custom, the capital stock K by previous in-

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Table 5.1 Basic macro relationships for a one-sector model

Markup Pricing NeoclassicalCost Function

P = (1 t)wb = wb/(1 − π) P = f(w, rP) (1)

L/X = b L/X = fω(ω, r) (2)

u = X/K u = X/K (3)

r = [τ/(1 + τ)]u = πu K/X = fr(ω, r) (4)

Macroeconomic Balance

gs = [sππ + sw(1 − π)]u = s(π)u (5)

gi = gi(r, u) = gi(π, u) (6)

= g0 + αr + βu = g0 + (απ + β)uγg + gi − gs = 0 (7)

Definitions

π = rPK/PX = τ/(1 + τ)ω = w/P = (1 − π)/bγg = PG/PK

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vestment, and government spending G and (for the given K) the spend-ing ratio γg = G/K by policy. Then with a fixed markup rate τ, the pricelevel P and the income distribution follow from (1). The demand equa-tions (5)–(7) and the distributional identity (4) jointly determine r and u.Output X follows from (3) and employment L from (2). We have amacro system in which causality runs toward employment and outputfrom the side of demand; output is implicitly assumed to lie below thefull capacity level κK determined by the available capital stock, where κis a “technically determined” capacity/capital ratio.

The neoclassical story is similar, but more tightly constrained. Only γg,w, and K can be predetermined—distributional variables such as τ, theprofit share π, and the real wage ω are endogenous to the system. Thiscomplication is reflected in the fact that (1) must be combined with (4)–(7) to solve jointly for u, r, and ω. Output and employment follow from(3) and (2) as before, while (1) gives the price level. As we have seen, oneinterpretation (essentially Keynes’s interpretation) is that the real side ofthe model underlying The General Theory comprises the neoclassicalequations (1)–(7) closed from the side of demand. Graphical illustrationsappear below and in Chapter 4.

Comparative statics of the two versions can be illustrated with threeexperiments: changing government dis-saving γg, the money wage w, andthe real wage ω. In both versions, a higher value of γg raises u and Xthrough a multiplier process that converges so long as saving supply in-creases more strongly than investment demand as a function of u—theHarrodian stability condition already explored in Chapter 4.

In the neoclassical model, (1) can be inserted into (4) to eliminate ω.The upshot is a positive relationship between r and u. But then from (1)stated as a wage-profit curve

1 = f(ω, r), (8)

ω must fall as u goes up. As observed in Chapters 2 and 4, this “first clas-sical postulate” implies that an increased demand injection is associatedwith greater output and a lower real wage, with decreasing returns set-ting in as more labor is combined with the available capital stock. Sincethe nominal wage is fixed, P must rise to reduce ω—the demand injec-tion drives up the price level as well as the output.

Neither the real wage decrease nor the price increase occurs in themarkup model, since τ is set from the outside and diminishing returns donot set in so long as capacity exceeds output. A demand injection couldeven cause real wage increases and price deflation (at least with respectto money wages) if the markup rate is an inverse function of u, as dis-

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cussed in Chapter 2. Empirically, this sort of response to rising output isnot unknown.

A change in the money wage w has no real effects in the markup sys-tem. From (1), P just adjusts in proportion, and the real side is un-changed. The neoclassical equations can easily be seen to depend only onω or w/P; therefore the same conclusion applies. For a given demand in-jection γg, the real wage is an outcome of the neoclassical model. Hencemoney wage changes will affect only the price level and not employment.This is basically Keynes’s argument about the uselessness of money wagereduction in Chapter 19 of The General Theory, presented in detail inChapter 4 above.

Because the real wage is endogenous in the neoclassical system, itcannot be shifted exogenously in a thought experiment. In the markupmodel, if the markup rate τ is changed by macroeconomic shocks or pol-icy (price controls, revised public enterprise charges, trade policy, and soon), the real wage will also move. As noted in Chapter 4, a real wage in-crease may make effective demand go either up or down. The latter,“profit-led” case arises when there is a small differential between ren-tiers’ and workers’ saving shares and/or the responsiveness of invest-ment demand to the profit share is strong. Such conditions are importantto determining stability of the adjustment mechanism we are about todiscuss.

Forced Saving

Forced saving occurs when u and X cannot vary, for example, be-cause the economy is using all its available capacity (u is at its “techni-cal” maximum κ) or employment L is predetermined at a “full” levelfrom the second classical postulate. In what follows, we concentrate onclosure by a fixed L along the lines of Kaldor (1956), but the analysis ex-tends to a supply-side restriction on output due to available capital or alabor supply function such as L = L(ω, X, K). A “surplus labor” speci-fication, for example, would make L highly elastic to the real wage, ef-fectively fixing ω. Such an assumption underlies a family of neo-Marxiangrowth models as illustrated graphically below.

In the markup model, setting employment adds a restriction to (1)–(7). In algebraic terms, the system becomes overdetermined, and somevariable must become endogenous to meet the new constraint. If in-cipient excess demand with fixed output leads to upward pressure onprices, the obvious candidate for endogeneity is the markup rate τ orprofit share π, and thereby the price level P from (1). The causal struc-ture is that L determines X in (2), and then (3) sets u. The demand equa-tions (5)–(7) give the profit rate r that balances saving and investment

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at the supply-determined level of u. The markup rate then comes from(4) and P from (1). Through price movements relative to the fixed moneywage (presupposing a greater saving propensity from profits thanwages), the income distribution adjusts endogenously to force the cre-ation of enough saving to meet the new injection of demand.

In the neoclassical version, (1) and (4)–(7) determine u, r, and ω as inthe output adjustment closure. But then the model falls apart. Equations(2) and (3) give inconsistent values for X—the only recourse is that oneequation be dropped. Two excisions generally appear in the literature.The first is to leave out the investment demand function, with implica-tions to be taken up below. The other is to omit (2) and replace (4) bythe identity r = πu. These moves are tantamount to abandoning mar-ginal productivity input demand functions and returning to the markupsystem.

This forced retreat underscores Kaldor’s (1956) doubts about the use-fulness of macroeconomic distribution theory based on marginal pro-ductivity; it also illustrates why implementation of a Schumpeterian in-novation via credit creation and forced saving is a disequilibrium processfrom the neoclassical point of view. Alternatively, forced saving can beseen as a macro adjustment scenario in which the neoclassical combina-tion of output and price increases in response to higher demand degener-ates into a pure price (and distribution) change when output is deter-mined from the side of supply.

This last observation leads into comparative statics in the markupmodel. With u fixed, if the demand injection γg increases, then in (5)–(7)the profit rate is the free variable that goes up to provide the correspond-ing saving supply. From (4) and (1), the markup and price level rise andthe real wage goes down. Reduced real spending on the part of wageearners caused by higher prices is the adjustment vehicle.

An obvious question is whether this adjustment process is stable. Fig-ure 4.2 already shows that it converges only when demand is wage-led,but it is worthwhile to demonstrate this result formally. With u predeter-mined, we can solve the model of Table 5.1 for π as

π =γ β

απ

g w

w

g s u

s s u

+ + −

− +0 ( )

[ ( )]. (9)

The macroeconomic stability condition with π as the adjusting vari-able in the short run is ∂(gi − gs)/∂π < 0. Mindless differentiation basedon the linearized investment function in the second lines of (6) showsthat this inequality is equivalent to

sπ − (sw + α) > 0, (10)

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or that the denominator in (9) is positive. Consulting the discussion ofequation (15) in Chapter 4 shows that condition (10) describes an econ-omy in which effective demand is wage-led if output is the adjusting vari-able. In the present context, the message is that instability occurs whenan increase in π sets off demand pressures which make it increase furtherstill, as in the “Harrodian hyperinflation” section ZC of Figure 4.2.1 Ifadjustment is stable, then contemplation of (9) shows that ∂π/∂sπ < 0.This is the standard “widow’s cruse” result of forced-saving macro mod-els—a reduction in the saving rate from profits makes the profit sharego up.2

Because π follows from effective demand, a money wage increasewould just drive up the price level proportionally under forced saving. Asimilar outcome could befall an attempt at redistribution. Suppose in asimple case that sw = 0, investment is stable at the level Ä, and that a taxtrPK is levied on profit income and transferred to wage earners. Saving-investment balance becomes r = Ä/sr(1 − t). The profit rate rises alongwith the tax rate increase, and the real wage correspondingly falls.

Real income per worker after the transfer is Yw = Ú + trK/L. Substi-tuting from the expression for r above and drawing on Table 5.1, onecan show that Yw = (1/b)[1 − (Ä/su)], independent of the tax-cum-trans-fer rate t. The transfer does not go through, in a reverse example of thewidow’s cruse. The cruse bedevils any transfer attempt when output is atan upper bound.

In closing, note that although forced saving has been described herein terms of wages and profits, similar redistributive effects can occuramong any savings flows. Applied models will include saving from thebusiness sector, one or more household income classes, the rest of theworld, and the government. Movements in financial surpluses (savingless investment) as prices shift will differ across these classes and institu-tions, allowing forced saving to occur. The presence of flows fixed innominal terms—transfers and state spending are common examples—makes redistribution induced by changing prices even more important.

Loanable Funds

Changes in “the” interest rate (say i, ignoring the real/nominaldistinction for the moment) mediate the adjustment mechanism alreadydiscussed at length in connection with the Ramsey/Tobin-q optimal ac-cumulation and Wicksell cumulative process inflation models. If savingincreases as a function of i,3 while investment demand gi declines, theneven with u and/or X predetermined, all seven equations of Table 5.1compose a well-behaved system. An exogenous increase in γg will make

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the left-hand side of (7) positive, and i will increase to restore equilib-rium by cutting investment and inducing extra saving.

This loanable funds story sounds sensible, but is subject to at least twoobjections (both emphasized by Keynes). The first, already discussed inChapter 4, is structural. Rates of return to assets in principle are deter-mined in markets for stocks, not by savings and investment flows. Thesecond question is about the strength of interest rate effects. As we haveseen, there is not much evidence anywhere that overall saving respondsto interest rate movements (although portfolio compositions certainlydo). With much investment controlled by the state and large enterpriseswith good access to finance, interest rate effects on aggregate demandmay be limited to only part of gross capital formation (housing construc-tion?) and perhaps consumer purchases of durable goods. Empiricalquestions arise, but low elasticities can cripple adjustment based on in-terest rate movements in and of themselves. They may have more wide-spread effects by inducing changes in asset prices, but the underlyingprocesses of arbitrage among own-rates of return only sometimes appearto be important in macroeconomic terms. Japan after its bubble burst isan obvious case in which they were. Will the United States in the decadeof the aughts be another?

IS/LM

These empirical worries are to an extent dispelled if the interestrate is not forced to be the only variable equilibrating injections andleakages in (7). Rather, i itself can emerge from some behavioral equa-tion and then help determine the levels of gs and (especially) gi, with out-put changes bearing the major burden of macroeconomic adjustment. Asdiscussed in Chapter 4, this sort of causal scheme appears to be whatKeynes principally had in mind when he wrote The General Theory. Al-though Keynes did mention them in his narrative, the subsequent main-stream emphasis on feedback effects involving u via a money demandequation

µ(i, u)[qPK/T) + 1] − ζ(Tc /T) = 0

as well as making saving a function of the interest rate are the handiworkof Hicks. In a streamlined setup where bonds issued by firms and thegovernment (both paying an interest rate i) are the only nonmonetaryfinancial claims, the asset price q is given by q = r/i = πu/i so that moneydemand can be restated as

µ(i, u)[(πuZ/i) + 1] − ζ(Tc /T) = 0, (11)

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where the state variable Z = PK/T is fixed at any point in time.Equation (11) is a simplified version of (34) in Chapter 4, dropping the

return to holding equity iv as an argument of µ.4 How it interacts with anIS curve to generate macro equilibrium has already been discussed. Thenovelty in (11) is that by bidding up q, a higher profit share will increasemoney demand and thereby the interest rate—financial responses canpush the economy in the direction of being wage-led. For growth theory,a key question is how the stock ratio or state variable PK/T evolves overtime. The analysis is presented in Chapter 7.

The Real Balance Effect

If output is predetermined and there is an independent investmentfunction, consumption is the main demand component that must vary topermit macro equilibrium. If consumer demand is an inverse function ofthe price level so that the aggregate demand curve slopes downward inthe (X, P) or (u, P) plane, the outcomes are straightforward: increasedinvestment crowds out consumption by driving prices up. As noted inChapter 4, forced saving provides such a linkage, but it lost theoreticalfavor (apart from Kaldor and colleagues) fifty or sixty years ago. In con-temporary macroeconomics, its place is taken by the real balance effect.The story is familiar, although as we have seen it leads toward an over-determined model in a neoclassical specification. Adjustment pivots onan exogenous money supply, M. A price increase will reduce nationalwealth by eroding real balances M/P. Wealth-holders might be expectedto try to restore their position by saving more; hence the overall savingrate becomes s = s(M/P). A higher P cuts consumption by increasing s.Crowding out by rising prices becomes feasible again.

Comparative statics of the real balance effect were worked out inChapter 4. The key result in a markup model is that money-wage cutscan raise output from the demand side by reducing P—this is the reasonwhy the real balance story is congenial to the mainstream. With neoclas-sical price formation, an even stronger result emerges. Marginal produc-tivity rules plus full employment determine the real wage w/P. But if Pvaries to bring aggregate demand into line with predetermined supply byaltering real balances, then there is no room in the neoclassical specifica-tion for independent determination of the money wage w. How wagechanges are neutralized by neoclassicists in the long run is a major themeof Chapter 6.

The Inflation Tax

The inflation tax is a dynamic version of the real balance effect,analyzed in Chapter 3. Its demand-reducing effect at times is practically

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relevant, for example in the consumption surges that have followed at-tempts to stabilize inflations by banning indexed contracts and imposingprice controls in heterodox shock anti-inflation programs in Israel, east-ern Europe, and Latin America. For that reason, it makes sense to mergean inflation tax with structuralist inflation theories emphasizing distrib-utive conflict and propagation mechanisms in applied models (Taylor1991, 1994).

Other Effects of Inflation on Demand

Inflation may affect other demand injections or leakages. Sup-pose that i, the nominal loan rate of interest, is pegged or comes fromthe financial side of the economy. Then faster inflation reduces the realrate i − ¾, perhaps stimulating capital formation via the Mundell-Tobineffect mentioned in Chapter 3. Contrariwise, by adding to fundamentaleconomic uncertainty, inflation may reduce capital formation. If eitherpossibility is deemed relevant, it is easily built into an investment func-tion. The same observation applies to effects of inflation on competitiveimports, demand for consumer durables, the efficiency of tax collection,5

or other variables.

Determination of Investment by Saving

Forced saving, loanable funds, and real balance effects providemeans for accommodating a labor supply function into the macro sys-tem. Dropping the independent investment demand function (6) isanother, as pointed out in Chapter 1. This artifice is widely used. Forexample, it is at the heart of Solow’s (1956) neoclassical growth modelanalyzed in the following section.

Causal links are straightforward. In the markup model, K, L, w, and τare predetermined. In Table 5.1, P comes from (1), X from (2), u from(3), r from (4), and gs from (5). In a savings-driven economy there is noroom for (6), so that capital stock growth gi comes from (7). The solu-tion of the neoclassical version is similar, except that as usual there is noroom for a predetermined distributive index such as τ. With w fixed,equations (1)–(4) solve jointly for P, X, r, and u, and the story thereaftergoes as in the markup model.

Output, income distribution, and saving all come from the supply sidein the neoclassical version of this closure, which emphasizes productivityand thrift. A higher value of γg reduces gi from (7). In the key rationalefor President Clinton’s fiscal policy of the 1990s, government spending“crowds out” investment demand. The real wage can’t be altered, and amoney-wage increase reflects itself solely in higher prices.

The markup model also demonstrates a pure price increase from a

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higher money wage and investment crowding-out by γg. A real wage in-crease is represented by a lower τ. From (4) and (5), the profit rate andsaving supply fall. Hence, (7) shows that the growth rate must decline.Such outcomes are opposite those in the output adjustment closure dis-cussed above. To reiterate, with potential results so different, empiricalawareness and institutional understanding of the economy are requiredto judge how an apposite macro model should be closed.

Adding Endogenous Variables to the System

Finally, suppose that the investment demand function (6) in Table5.1 is reinstated along with predetermined employment, but that γg is en-dogenous. Then all equations can be retained, with γg coming from (7).The interpretation is that the government regulates its spending to en-sure full employment. Another possibility would be for the governmentto adjust some tax variable (though not the ineffective rate t of the tax-cum-transfer program discussed above) to the same end. The spendingscenario is spelled out in Meade (1961), while Johansen (1960), when heset up the first-ever computable general equilibrium model, used an en-dogenous income tax to accommodate both an independent investmentfunction and full employment.

2. Graphical Representations and Supply-Driven Growth

The foregoing arguments are easy to summarize in diagrams. The pic-tures used here are complementary to those in Chapter Four. We first de-scribe equilibrium in the short run, and then show how growth modelsconverging (at times) to steady-state solutions emerge from the variousclosures.

Figure 5.1 illustrates macro equilibrium under a markup pricing speci-fication, using the linearized version of the investment function in thesecond line of (6).

The topmost quadrant to the right plots capital stock growth as afunction of the profit rate. Equilibrium is defined by the intersection ofthe schedules for saving leakages gs and demand injections gi + γg (twolevels of investment demand, labeled by subscripts, are shown). In thequadrant just below, capacity use is related to the profit rate by the rule r= πu until a capacity limit Ä is reached at a profit rate ¨. To the left of thekink at Ä, r and π vary independently of u. To the right, u = Ä and the in-vestment functions become sensitive to variations in π only in the profitrate identity r = πu. Hence they are less steep as functions of r.

The lowest quadrant shows that the real wage ω (and therefore the

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markup rate τ and profit share π) is constant for u ≤ Ä and r ≤ ¨. To theright of the kink, ω becomes a decreasing function of r as forced savingapplies with a binding output constraint. Finally, in the quadrant to theleft, the labor/capital ratio L/K = bu increases with u until u = Ä. Forlater use, let λ stand for L/K.

The intersection of g i1 + γg with gs depicts a closure in which output

adjustment reigns. A small increase in γg will shift the injection scheduleup, leading g, u, and λ to rise with a constant real wage. With a predeter-mined π, the macro equilibrium will be stable when condition (14) inChapter 4 applies. An overly strong investment response to an increasein u can create short-run instability. Figure 5.1 shows the stable case; in-stability would require g i

1 + γg to have a steeper slope than gs.The intersection of g i

2 + γg with gs corresponds to a forced savingmodel with r > ¨. A higher γg initially shifts the injection schedule up-ward, leading g and r to rise while ω declines. Final equilibrium isreached after a further readjustment of g i

2 + γg induced by the rise in πcorresponding to the lower real wage. The new solution will be stable inthe short run when condition (10) is satisfied.

model closure and growth 183

u

gs

gig2 + γ

r Profit rate r

Output/capitalratio u

Real wage ω

Capital stockgrowth rate g

Labor/capital ratio λ

λ = bu¯

¯

r u= π

gig1 + γ

Figure 5.1Markup macroeco-nomic equilibrium.

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The model with neoclassical price formation is illustrated in the right-hand quadrants in Figure 5.2; the story combines output and forced sav-ing adjustments as discussed above. The main contrast with Figure 5.1 isthat the kinks at u= Ä and r= ¨ have been replaced by smooth curves in-dicating that the profit rate is an increasing function of capacity utiliza-tion, while r and ω trade off inversely along the factor price frontier. Anincrease in γg now leads g, r, and u to rise and ω to decline.

The quadrant to the left shows that u (= X/K) rises smoothly withthe labor/capital ratio λ along a neoclassical production function. Thisobservation becomes of interest when we switch closures in the model.Suppose that instead of reading Figure 5.2 clockwise in an investment-determined scenario, we trace causality counterclockwise from a prede-termined level of λ. Now u follows from the identity λ = bu, determiningr which in turn sets ω and gs. As we have already noted, there is no roomin this reading for an independent investment function: gi must adjust tosatisfy the macro balance condition gi + γg − gs =0. The injection sched-

184 chapter five

gig+γ

Real wage ω

Capital stockgrowth rate g

Profit rate r

Labor/capital ratio λ

Output/capitalratio u

CapacityutilizationProduction

function

gs

Figure 5.2Neoclassical macro-economic equilib-rium.

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ule gi + γg can be viewed as sliding up and down until it meets gs at thesupply-determined profit rate r. As we will see, the resulting capital stockgrowth rate g varies to ensure steady-state stability in Solow’s (1956)mainstream standard model.

Stories about Steady States

Contemporary economists use one or the other of two approachesto formal stability analysis in macro growth models. The one adoptedheretofore in this book (except for the OLG model in Chapter 3) in-volves perfect foresight leaps between saddlepaths on the part of someflow or control variable(s) while the state variable(s) stay constant in an“instant” of time. This way of doing dynamics became popular in the1970s, when saddlepoint “instability” in dynamic optimizing modelswas miraculously transformed into “stability” via jumps in control vari-ables at initial time points induced via “backward” differential equa-tions for costate variables subject to transversality conditions at finaltimes. How long the jumps stay fashionable remains to be seen. The sce-narios we have looked at so far suggest that intelligent leapers may plau-sibly land on their feet in the short run, but almost certainly not overendless stretches of time.

The more traditional approach followed by Solow, Kaldor, and manyothers is to assume that short-run variables such as the ones pictured inFigures 5.1 and 5.2 converge “rapidly” to equilibrium. The behavioralrelationships satisfied by the “fast” variables shift in response to changesin “slow” or “state” variables set up as ratios of two growing quantities.The time derivative of each state variable comes from short run equilib-rium, and when it is equal to zero, both the numerator and the denomi-nator will be growing at the same rate—this is a steady state which canbe used to characterize the economy “in the long run.” Two exercises instability analysis are built into this procedure—for the short-run adjust-ment and the steady state. The implicit time frame for the former mightbe months or quarters, and years or decades for the steady state. Presum-ably a steady state is not worth investigating if the economy is not stablein the short run.6

The Solow Growth Model

One interpretation of Solow and Kaldor is that they proposedtheir growth models as a means to bring a growth rate gw “warranted”by short-term macro balance into equality line with a “natural” growthrate n via shifts in the capital/labor ratio and the overall saving rate re-spectively. These maneuvers were supposed to let the economy avoid

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Harrod’s “knife-edge” discussed below. This interpretation works betterfor Solow, although it is easy to argue that he did not so much avoid asignore Harrod’s investment-driven causal scheme. Be that as it may, hismodel has been put to many uses and merits examination on its ownterms.

For the Solow model, K/L is usually used as the state variable. Thatprocedure is adopted here in Chapter 9 when the model is reintroducedto lead into Tobin’s monetary growth and cycle theory. But since it al-ready appears in Figures 5.1 and 5.2, we can just as well work with theinverse λ = L/K. The relevant differential equation is

Ö = λ[ü − g(λ)] = λ[n − g(λ)], (12)

where the employment (= population) growth rate n = ü is taken as pre-determined.

Suppose that g < n. Then Ö > 0, and the consequent increase in λ willlead in Figure 5.2 to higher values of u, r, and g in the counterclockwisereading. The upshot of this short-run adjustment is that g is an increas-ing function of λ, so that in equation (12) dÖ/dλ < 0 around the long-runrest point where g = n. The implications are that λ is locally stable, andthat marginal productivity rules and the cost function determine thelong-run income distribution from the level of λ at steady state.

Solow emphasized the role of real wage (and more generally, price) ad-justment in leading to full employment in the short run. However, Figure5.2 suggests that wage changes are a sideshow in the southeast corner. Inthe constant markup area of Figure 5.1 (with causality running counter-clockwise and the independent investment function suppressed), it canbe seen that a reduction in λ will lead u, r, and g to decline in the shortrun. Steady-state growth equilibrium is stable in a price-insensitive sav-ing-driven model. Short- and long-run distribution both follow from thepredetermined markup rate τ.

The moral is that the key to stability in saving-driven models is the de-termination of accumulation by saving supply as an increasing functionof capacity utilization or the profit rate, not flexible prices. If the savingrate is a decreasing function of the profit rate, the growth process can beunstable as we saw in the OLG model in Chapter 3.

Along with the Ramsey model, Solow’s story is the workhorse ofmainstream growth theory. It has figured recently in the debate over en-dogenous growth that is touched upon in Chapter 11. A few points areworth introducing here.

Away from the steady state at which Ö = 0 and λ = λ*, the model saysthat the labor/capital ratio will be falling more rapidly, the higher the

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level of λ. That is, growth of capital and output per worker will be faster,the poorer the economy. This prediction is counterfactual in that coun-tries which do manage to enter into sustained economic growth usuallydo so at a faster rate at middle income levels of a few thousand dollarsper capita. Japan’s extremely rapid labor productivity growth during itscatch-up phase toward the left side of Figure 2.1 is the classic example.

More generally, growth accounting in the Solow framework boilsdown to applications of equations (10) and (12) in Chapter 2 acrosstime. In purchasing power parity terms, real income levels per capita inrich countries are on the order of ten times as high as they are in poorones. To examine potential sources of this discrepancy, we can restateequation (12À) from Chapter 2 as

¼ − ü = (1 − ψ)(ú − ü) + ψÀL + (1 − ψ)ÀK, (13)

where ψ is the labor share and ÀL and ÀK are the growth rates of labor andcapital productivity respectively. If we let ξL and ξK stand for productiv-ity levels and hold ψ constant (implicitly slipping in a Cobb-Douglas ap-proximation), then integrating this differential expression gives

X/L = (K/L)1−ψ(ξL)ψ(ξK)1−ψ (14)

as an equation for per capita output.It is not easy to measure ψ in poor countries, because much economic

activity is undertaken by independent proprietors (peasants, petty trad-ers, and so on) who receive diverse blends of “wage” and “profit” in-comes. However, a consensus view is that ψ is well less than 0.5 in a verypoor economy and perhaps 0.8 in a rich one (recall Table 1.4). If ψ were,say, 2/3, then if a tenfold difference in income per capita were to be ex-plained only by variation in the capital/labor ratio, K/L would have to be103 = 1,000 times as high in the rich country as in the poor one. Such adifferential (and on neoclassical grounds a correspondingly enormousprofit rate spread) is not observed. A labor productivity differential of103/2 = 31.6 would suffice, as would combined capital/labor ratio and la-bor productivity differentials of ten each (all assuming no capital pro-ductivity differential or Marx bias). A principal concern of contempo-rary mainstream growth theorists is to “explain” how cross-countrylabor productivity differentials on the order of ten can possibly arise.Their most recent ploys are to enhance the importance of saving andthrift by invoking accumulation of “human,” “intangible,” “organiza-tional” or other forms of capital which are supposed to raise ξL, to rede-fine the accounting to raise the capital contribution 1 − ψ, or both. SeeChapter 11 for some details.

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A Kaldor Growth Model

Decades in advance of the contemporary mainstream, Kaldor(1957) was concerned with the role of endogenous technical change ingrowth. He also wanted an independent investment function and fullemployment of labor. As discussed above, in the short run forced sav-ing permits the investment function and full employment to coexist.Kaldor’s model is a dynamic extension of this closure, coupled with his“technical progress function.”

The short-run story can be read from Figure 5.1. Capacity utilizationu follows from the full employment level of λ in a counterclockwise read-ing of the southwest quadrant based on the relationships u = λ/b = ξLλ.The capital stock growth rate and the profit rate and share are deter-mined by the intersection of g i

2+ γg with gs, as outlined above. For usebelow, the explicit solution for the growth rate is

g =( )( ) ( )

( )s s g u s u

s sw g w

w

π

π

β α γ

α

− + + −

− +0

(15)

Kaldor’s (1961) stylized facts about advanced economies included astable output/capital ratio and profit rate combined with steady in-creases in labor productivity and the capital/labor ratio over time. Alongthe lines of the Verdoorn (1949) and Okun (1962) “Laws” mentioned inChapter 2, he bundled the latter two observations into a “technicalprogress function” for labor productivity, ξL = f(K/L). In growth rateform,

ÕL = ÀL = φ0 + φ1(g − n). (16)

The natural state variable for the Kaldor model is the output/capitalratio u. If its differential equation is stable, u presumably will not be ob-served differing greatly from its value at steady state, fitting the stylizedfact. Since u = ξLλ, using (16) the time derivative Í is given by

Í = u[(1 − φ1)(n − g) + φ0]. (17)

Old-fashioned stability analysis is based on the hypothesis that 0 < φ1

< 1, so that labor productivity growth in (16) does not generate its ownknife-edge. We then have dÍ/du < 0 when dg/du > 0 from (15). With apositive denominator in this formula (the short-run forced saving adjust-ment process is stable from (10) because aggregate demand is wage-led),dg/du > 0 when (sπ − sw)β − αsw > 0, or there is a big difference in sav-ing propensities and the accelerator coefficient β is large. From Chapter4, these are just the conditions required for growth to be wage-led in an

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economy where output is the adjusting variable. Forced saving supportssteady-state stability when both the output/capital ratio and the capitalstock growth rate are wage-led.

From (17), the long-run, natural rate of growth when Í = 0 is

g = n + φ0/(1 − φ1),

which depends only on population expansion and the parameters of thetechnical progress function. The steady-state output/capital ratio andprofit share follow from the conditions for short-term equilibrium. In awidely discussed special case, if there is no government dis-saving (γg =0) and sw = 0, then the “Cambridge equation” (simplified from (5) in Ta-ble 5.1)

g = sππu = sπr (18)

determines long-run income distribution from the steady-state values ofr, π, and u. Moreover, because π = 1 − ωb = 1 − ω/ξL and is constant,we have Û = ÀL, or the real wage increases at the rate of labor productiv-ity growth. This 100 percent pass-through of productivity gains into realwage increases is characteristic of growth model steady states whichhold factor shares constant. It shows up in the Solow and Ramsey for-mulations as well.7

In the spirit of his times, Kaldor concentrated on such steady-stateoutcomes, rather than on the possibilities of “endogenous” growth orcontraction occurring in the dynamically unstable case when φ1 > 1.Such possibilities are examined in Chapter 11.

Marxist Models

For reasons sketched in Chapter 11, it is extremely difficult toshoehorn Marx into simple formal models. Regardless, people continueto try. One example is another counterclockwise reading of Figure 5.2which fixes the real wage in the southeast quadrant, say from “classstruggle”—see Sen (1963), Marglin (1984), and Dutt (1990). Again,there is no room for an independent investment function, as u, λ, r, and gall follow from ω. Capital stock growth g will in general not be the sameas the natural growth rate n, which eventually may lead the model tobreak down.8

One problem with this formulation is that Marx was well aware of therole played by technological change in generating crises and growth. Ifthere is labor productivity growth and a fixed real wage, equation (10) inChapter 2 already shows that the profit rate would have to trend steadilyupward—a tendency that is never observed. From a Marxist perspec-

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tive, a model with a predetermined wage share as opposed to Sen’s fixedreal wage is a more appropriate vehicle for the analysis of productivitygrowth. Foley and Michl (1999) develop such a specification and workthrough several applications. Their setup is consistent with the cyclicalgrowth models analyzed in Chapter 9.

3. Harrod, Robinson, and Related Stories

Growth models driven from the side of demand are much less commonthan their supply-side cousins in the literature. Nevertheless, they haveconsiderable intrinsic interest, and also serve as the framework for muchof the analysis in Chapters 7–11. We present an introduction here, begin-ning with the controversy over Harrod’s instability problem and then go-ing on to the more stable formulation used in the rest of the book.

As noted above, Solow seems in part to have seen his dynamics asa means of getting around the “knife-edge” that Harrod (1939) em-phasized in his pioneering growth model. That is, for Solow λ adjustssmoothly to let the capital stock growth rate g(λ) converge to labor forcegrowth n. As we have seen, the basic mechanism is a counterclockwisereading of Figures 5.1 and 5.2.

Harrod, as it turns out, was a clockwise economist. His knife-edgeexists not because saving drives investment but because causality runsthe other way and the investment function is rambunctious enough tocause long-term instability. We can fill in some details and also discussanother potentially unstable investment-driven model proposed by Rob-inson (1956).

Harrod’s paper is not easy to read, and contains no explicit model. Forthat reason, three proposed formalizations are quickly presented here. Inthe first, due to Barbosa-Filho (2001a), output is the short-run adjustingvariable (which can jump), and the capital stock grows steadily overtime. For reasons to be made clear soon, it is interesting to carry “auton-omous” real expenditures A as a component of demand, X = C + I + A.The variable A could comprise the intercept term in a Keynesian con-sumption function, government spending, net exports, and so on. With a= A/K, g = I/K = ú, and s as the overall saving rate, macro balancetakes the form su = g + a in a slight extension of the familiar “Harrod-Domar” equation. By simple differentiation, it is also true that

dg/dt = g(Æ − g) (19)

and

da/dt = a(Â − g). (20)

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This system of equations has a nontrivial solution only when Æ = Â = g,that is, the growth rates of investment, autonomous spending, and cap-ital are all equal. In the discussion to follow, Â is treated as a predeter-mined “forcing” variable in (19)–(20).

A standard interpretation of Harrod is that his model is based onstrong accelerator dynamics, say

Æ = f(u) = f [(g + a)/s] (21)

with f as an increasing function.9 On this hypothesis, the Jacobian of(19) and (20) evaluated at a stationary point becomes

Jg f s gf s

a=

′ − ′−

[( / ) ] /10

,

in which f′ = df/du.The system will be stable when f′ < s, in a dynamic analog to the

usual Keynesian stability condition discussed in Chapter 4. If this in-equality is violated, the variables will follow a diverging counterclock-wise spiral in the (g, a) plane, along lines discussed in Chapter 9. The for-mulation captures at least part of what Harrod had in mind with hisknife-edge. An overly strong investment response can easily push thegrowth rate away from its steady state value Â.

If the model is stable, the autonomous spending term can be used toaddress concerns raised during the 1930s by “secular stagnationist”Keynesians like Hansen (1938). They thought that active fiscal policywould be needed to offset what they saw as a long-term collapse in in-vestment demand. It is easy to see that an increase in the growth rateof autonomous spending  will increase the long-term economy-widerate of growth in (19) and (20). Hansen did not foresee how “militaryKeynesianism” during and after World War II would make his fiscalworries disappear.

Besides thinking about accelerators, Harrod also contrasted the natu-ral growth rate n with a “warranted” capital stock growth rate gw. To seewhat he may have had in mind, it is simplest to drop autonomous spend-ing and to define variables relative to the labor force (and population).The output/labor ratio (or average labor productivity) is ξL = X/L, in-vestment per worker is ι = I/L, and k = K/L is the capital stock per cap-ita. The per capita macro demand balance is ξL = (1 − s)ξL + ι, whereagain s is the saving rate from output. Clearly, ξL = ι/s, and can jump inresponse to shifts in investment and saving rates. It is easy to see that

| = k(g − n) = ι − nk = sξL − nk. (22)

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A steady state exists when | = 0. Implications are that ι = sξL = nkand g = ι/k = sξL/k = s/µ, where µ = K/X is the capital/output ratio.10

The “warranted rate” is gw = su = s/µ. If savings equals investmentthanks to short-run market clearing (which may or may not have beenassumed by Harrod), the warranted rate will be the observed growthrate as well. In steady state, the warranted and natural rates are equal.Harrod’s question was, is such a steady state stable?

Once again, the answer could be no. As we have seen in (21), in whichÎ = (dI/dt)/I responds to g = I/K, one way to build instability into themodel is by positive feedback of investment demand into itself. For ex-ample, we can replace (6) with a function determining the change in in-vestment instead of its level. Suppose that firms have a target level of out-put per capita given by the expression ÔL = kÄ with Ä as a “normal” levelof the output/capital ratio (not necessarily equal to the steady state valuen/s). Then the investment function might be

di/dt = φ(ξL − ÔL) = φ[(ι/s) − kÄ] (23)

with φ as a response coefficient.The Jacobian of (22) and (23) is

Jn

=−−

1φ φu s/

with Tr J = (φ/s) − n and Det J = φ[(Ä − (n/s)]. Instability can show upin a couple of ways. First, if firms set their target output/capital ratio toolow, Ä < n/s, then Det J < 0 and there will be saddlepoint dynamics. Ifthe target output level is higher, Ä > n/s, then a moderately strong accel-erator coefficient, φ > sn, could destabilize the system. If Ä = ns exactly,(23) reduces to

è = (φ/s)(ι − nk) (23a)

so that Det J = 0 and the system is indeterminate. Since it incorporateschanges in investment rather than the capital stock, (23a) has “faster”dynamics than (22) and would presumably lead to instability if someshock perturbs the steady-state equality ι = nk.

This scenario seems to catch more of the essence of Harrod, althoughit suffers from relying on the specific investment function (23) and hav-ing an output/capital ratio that is endogenous as opposed to being “tech-nically determined” in the short run. A basically similar story is pro-posed by Sen (1970), with less emphasis on the natural rate and more onan investment function based on a Marx/Keynes dialectic between ex-pectations and realizations.

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Translating Sen’s analysis from discrete to continuous time, let Xstand for current output, Xr = X + †rδ for output to be “realized” ashort time δ from now, and Xe = X + †eδ for expected future output.The warranted rate is †r/X = s/µ with µ (or u) treated as a parameter in-stead of a variable as in the previous example. The warranted and natu-ral rates are implicitly assumed to be equal in an initial steady state.

More precisely, µ can be interpreted as a “marginal” capital/output ra-tio. Then investment demand is determined by an accelerator relation-ship I = µ†eδ so that X = I/s = (µ/s)†eδ. If †e = †r, the economy stayson the warranted growth path. Instability arises when it is somehowpushed away from this perfect foresight trajectory. To see the details, letgi = †i/X for i = r and e. A bit of algebra shows that

gr − ge = (µ/s)[(Xr − Xe)/X]ge.

If expected growth is stimulated when realizations outrun expecta-tions,

dge/dt = φ(gr − ge) = φ(µ/s)[(Xr − Xe)/X]ge (24)

then we have positive feedback of ge into itself and a knife-edge. Anysmall blip of Xr over Xe will make the right-hand side of (24) positiveand set off explosive growth. The investment equations (21), (23), and(24) all share a family relationship and give rise to similar dynamic out-comes.

Harrod-style assumptions can be used in the analysis of cycles (Shaikh1989) and also underlie much of “new” or “endogenous” growth the-ory (Chapter 11). However, they are counterfactual insofar as capitalisteconomies (not even Japan in the 1990s) are not observed to have rap-idly accelerating or decelerating rates of growth. A growth model withan accelerator investment function that can maintain a steady state wasproposed by Robinson (1956).

If all wage income is consumed, equation (5) in Table 5.1 shows thatfrom the side of saving the growth rate must satisfy the “Cambridgeequation” (18) introduced above. Suppose that the investment functiontakes the form

Å = φ[f(r) − r], (25)

in which f(r) gauges the extent to which entrepreneurs are stimulated togreater capital formation. When expected profits f(r) exceed the cost ofcapital r, they bid up the capital stock growth rate. Presumably, the in-centive diminishes as r goes up.

Appropriately drawn, (18) and (25) create “Joan Robinson’s banana”

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in Figure 5.3. The lower equilibrium at A is a knife-edge à la Harrod. Atpoint B, f(r) = r and f′(r) < 1, producing a stable steady state. We willsee in Chapter 9 how dynamic expectations about expected profits in themodel can generate cyclical growth.

4. More Stable Demand-Determined Growth

Sticking with an investment function of the form of (6), is it possible toconstruct growth models based on clockwise readings of Figures 5.1 and5.2? The answer is certainly in the affirmative—it makes perfect sense toconsider capital stock growth trajectories when there is an independentinvestment function and unemployment is possible in the long run (a“bastard golden age” in Joan Robinson’s (1956) terminology). At pres-ent, the existence of readily employable labor is not a bad assumption inmost economies of western Europe and is certainly a good one in the de-veloping world (especially for those countries afflicted with IMF-styleausterity programs in recent years). Over extended periods of time, out-put adjusting in Keynes/Kalecki fashion becomes an obvious closure toconsider.

Moreover, it is possible to bring in IS/LM by assuming that the invest-ment function takes the form

gi = g0 + αr + βu − θi = g0 + (απ + β)u − θi

194 chapter five

Profit rater

Capital stockgrowth rate g

Cambridgeequation

f(r)

B

A

Figure 5.3Joan Robinson’sbanana.

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as in previous chapters. Then in short-run equilibrium with an institu-tionally determined profit share π or wage share ψ = 1 − π, the reduced-form equations for capacity utilization and the capital stock growth rateare

ug i

sg

=+ −

− +0 γ θ

π απ β( ) ( )(26)

and

gs g i

sg

=+ + −

− +

( ) ( )( )( ) ( )

απ β γ π θ

π απ β0

(27)

where s(π) = sππ + sw(1 − π) from (5).There are several paths to be explored with (26) and (27). One in-

volves distribution as it emerges from productivity- and cost-based infla-tion dynamics. With the profit or wage share given at a point in time, g isa function of the interest rate i emerging from a short-run IS/LM systemcomprising (11) and (26). As we will see in the following chapters, thereare reasons to believe that distributive indicators change in response toseveral forces. As they move, then so will the growth rate. For example,in (27) g is both a direct and an indirect (through IS/LM) function of π orψ, which in turn evolves according to its own proper dynamics.

A steady state is reached in such a model when the dynamic processfor the wage share reaches a point at which Þ = 0. As already noted inChapter 4, g can vary across such steady states, which is not the casewith employment-constrained growth. Demand-driven growth modelsare useful for asking how certain policies affect prospects for sustainedeconomic expansion. A question relevant in developing countries, forexample, is whether there is a natural way for recently popular externalliberalization policy packages to lead an economy to socially acceptablerates of employment and growth. The observed answer to this particularquery very often seems to be no (Pieper and Taylor 1998; Taylor 2000).

Second, one can ask similar questions about monetary policy, usingequation (11), which includes the state variable Z = PK/T. The task is toconsider its evolution over time coupled with ψ in a two-dimensionalsystem, after solving for i, u, and g in (11), (26), and (27). Intriguing dy-namic scenarios can emerge from such systems, as we will see in Chap-ters 7 and 8.

Third, it is of interest to analyze pension schemes from a Keynesianperspective as opposed to the supply-determined OLG model of Chapter3 with its odd assumptions about saving. To keep the algebra withinbounds, we can assume a zero saving rate from wage income and ignore

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LM linkages. As in the OLG model, we work with cohorts of employ-able households Ht which work in period t and live off pension incomein period t + 1. At time t, overall macro balance can be written as

Xt = (1 − sπ)πXt + (1 − π)Xt − qHt + Zt + It.

Household numbers grow between periods at the rate n so that Ht+1 =(1 + n)Ht. In the period when they can work, all households (whetheremployed or not) are assessed an amount q which is used to finance pen-sions.11 Total social security disbursements to the retired population areZt. Both the households in the labor force and the retirees have zero sav-ings rates, so the pension program basically shifts resources from onehigh-consuming group to another.

A “pay-go” scheme in this model just uses contributions directly topay retirees, Zt = qHt, with no impact on effective demand. The numberof retirees is Ht /(1 + n) so their benefit per household is (1 + n)q, just asin the OLG model. The difference is that in an OLG world a pay-goscheme has visible effects on macro performance, whereas in a Keynes-ian world it doesn’t.

A fully funded scheme, in contrast, has effects on output and growthin the Keynesian model but not in the OLG. The total pension outlay inperiod t is Zt = q[Ht /(1 + n)](1 + rt), which need not be equal to qHt.That is, each of the Ht /(1 + n) employable households in period t − 1paid a contribution q which was invested to give them a return at the in-terest (= profit) rate rt. Let ηt = Ht /Kt. Then taking into account the ef-fects of the pension program, one can write out an expression analogousto (26) as follows:

sππ − (απ + β) − [πqηt /(1 + n)]ut = g0 − [nqηt/(1 + n)].

Letting B > 0 stand for the bracketed expression multiplying ut, onefinds that

dut = B−1[(rt − n)q/(1 + n)]dηt,

so a higher population/capital ratio ηt will raise capacity utilization ut

and growth gt = sππut when the profit rate exceeds the rate of populationgrowth (the empirically relevant case). The intuition is that the demandinjection from the pension investment “last period” is outrunning the in-creased leakage due to population growth. A similar condition will comeinto play when we consider debt dynamics in Chapter 6.

It will also be true that

ηt+1 = ηt1 + (1 + gt)(n − gt)]. (28)

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At an initial steady state with ηt+1 = ηt = η*, the warranted and naturalgrowth rates will have to be equal, gt = n. Differentiating (28) with re-spect to ηt and using this condition gives the result

dηt+1/dηt = 1 − ηt(1 + gt)(dgt /dηt).

For dynamic stability we need dηt+1 /dηt < 1. This condition can applyif dgt/dηt > 0, which from the discussion above appears to be the case.The dynamic analysis will be the same as in the upper diagram of Figure3.5. One can ask, for example, what will happen if the scale of the pen-sion scheme is expanded via an increase in q. With rt > n, it is easy to seethat there will be an increase in effective demand and output growth inthe short run. The accumulation locus will shift downward, leading to anew, lower value of η*. The shift signals a higher level of capital perhousehold, or a richer population. In Keynesian models, long-run out-comes of pension schemes and all other fiscal innovations are driven bythe paradox of thrift. The effects of the policy change are 180 degrees re-moved from those emerging from the OLG model in Chapter 3.

This sort of outcome leads to one last question about demand-deter-mined models. It implies that there are no “normal” long-term levels ofcapacity utilization u, the capital stock growth rate g, and the steady-state household/capital ratio η*. Such results seem to bother a lot of peo-ple, and set off a debate summarized by Lavoie (1995). The central ques-tions appear to be (1) whether it makes sense to postulate that a “naturalrate” of capacity utilization u* exists, and (2) if it does exist what forceswill make u converge to u* in the long run?

With regard to the second question at least two answers show up inrecent literature. One involves modifying the investment function (6)in Table 5.1 to make gi depend on a term such as (u − un), where un

stands for normal capacity use. Following Lavoie, if one further postu-lates adaptive evolution for un,

Ín = ρ(u − un),

as well as for the animal spirits term g0 in the investment function,

Å0 = µ(g − g0)

then Dutt (1997) shows that this two-dimensional system will end up ata point where u = un. The equilibrium values of g0 and un will depend oninitial conditions, moreover, so that “history matters” in the determina-tion of economic performance.

Although no one seems to have done it, the Lavoie-Dutt specificationcould be combined with another approach suggested by Barbosa-Filho

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(2000). The central point is that u in (26) depends on various parametersand the profit share π. One could then set up dynamics on π to steer u to-ward a predetermined u* or an evolving un. Once again, capacity utiliza-tion would tend toward a “natural” or “normal” level.

Referring to the first question above, however, one can ask whethersuch a procedure makes modeling sense. As discussed in Chapters 7 and9, profit and wage shares have their own proper dynamics in terms ofwage and price inflation rates and the growth rate of productivity. It maybe more appropriate to work directly with such variables to determine along-run distributive equilibrium which can shift in response to eco-nomic forces. At the end of the day, structuralist models don’t blend hap-pily with natural rates.

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chapter six

z

Chicago Monetarism, New ClassicalMacroeconomics, and Mainstream Finance

In the mainstream’s eyes, ruling macroeconomic doctrines from the1960s through century’s end were built on the rubble from the neoclassi-cal demolition of the castle of Keynes. Before returning to structuralistanalysis, it makes sense to undertake a critical review of the new theoriesthat were constructed.

By around 1960, the main building blocks of The General Theory—the principle of effective demand and determination of output throughthe income-expenditure linkage (Clower’s “dual decision hypothesis”mentioned in Chapter 4)—had been effectively supplanted by the realbalance effect and determination of the value of output PX by the talis-manic letters MV.1 The counterrevolutionary task remaining was to re-store the second classical postulate and determine X by labor supply.

This operation took two stages. The first was the “natural rate” or“accelerationist” model advanced by Milton Friedman (1968) andEdmund Phelps (1968), and the second was the rational expectations/perfect market clearing hypothesis put forth by new classicists such asRobert Lucas (1972), Thomas Sargent (1973), and Robert Barro (1976).The difference between the two approaches is a matter of timing. Bothassert that macroeconomic equilibrium is determined by the first andsecond classical postulates, or the intersection of schedules for labor de-mand and supply derived from MIRA foundations. The natural ratemodel just makes convergence to this position run a little slower.

As previewed in Chapter 4, strong “policy ineffectiveness” proposi-tions emerge from both versions, basically because the economy can’tbe budged from its postulated “natural” stationary or steady state. Awidely debated extension of this fundamental new classical message isthe argument that bond and tax financing on the part of the governmentare equivalent—a translation of the Modigliani-Miller theorem to thepublic domain under the rubric of “Ricardian equivalence.”

The most recent thrust from the Right has been an effort (anticipatedmany decades previously by Marx, Schumpeter, Wicksell, and Hayek) to

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explain economic fluctuations from the supply side using “real businesscycle” models. Their formal foundation is stochastic dynamic optimiza-tion, which also underlies the mainstream finance results quoted in pre-vious chapters. The story here continues with reviews of these “pseudo-mathematical” reifications of the institutional complexities emphasizedthroughout this book.2 They lead naturally to a couple of proofs of theModigliani-Miller theorem, with which the chapter closes.

1. Methodological Caveats

Before we get into the algebra, a few general observations are in order.The first is that all new classical analysis is devoid of social content—therichly detailed capitalist world described by Keynes and Kalecki standsout by its absence.

The monetarist and rational expectations/perfect market clearingmodels’ only difference from a purely atomistic Walrasian scenario isthat information about prices and the money supply may take a while toget transmitted. In an “islands” parable advanced by Phelps (1969), forexample, corporations, financial houses, and organized labor don’t exist,because all production is in the hands of independent contractors (onefor each commodity) who live on semi-isolated islands. Each such agentis on its labor supply curve (the second classical postulate) and knowsthe price of the product it sells. However, knowledge of the general pricelevel travels at finite speed and picks up random “noise” while diffus-ing across islands. This “information asymmetry” is the sole source ofmacroeconomic dis-coordination. Other economic and social relationswithin and between islands don’t exist.

Second, the epistemology underlying the models oddly combines anAustrian insistence on the powers of entrepreneurship to cut throughmarket imperfections with a rigidly positivistic approach to the acquisi-tion of knowledge—this is the (post–Frank Knight) Chicago angle. Thecentral message of traditional Austrian economics that an unfetteredmarket is the best guarantor of human well-being is given a philosophi-cal twist more characteristic of the Vienna of Rudolf Carnap than ofCarl Menger—fundamental uncertainty about future events yields tostochastic perfect foresight.

As noted in Chapter 4, Knight, Keynes, and Hayek all thought thathuman decisions are made under conditions of unavoidable ignorance—there is no means by which complete probability distributions can be im-posed on the future. Indeed, the presence of uncertainty opens room forthe entrepreneur to maneuver. When people have different ideas aboutthe future, entrepreneurs can back their own judgments against those of

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others and succeed. They wouldn’t have the chance if we all held com-mon expectations and acted according to them in the same “rational”way (as the representative agent hypothesis suggests).

Keynes talked about “expectations” on almost every page of TheGeneral Theory, but (in roughly increasing order of precision) his use ofword meant something like “adivinations,” “anticipations,” or “views”about events to come. We have seen how he thought that attempts to cal-culate expected values of future happenings in a probabilistic sense wereworse than useless.

Knight’s and Hayek’s doubts and Keynes’s objections were over-thrown in the 1960s, when for most economists the meanings of “expec-tation” and “expected value” in the sense of probability theory becameidentical.3 Moreover, the ideas took hold that an “objective” model ofthe economy exists and that its structure is shared knowledge among allagents—concepts unthinkable to Knight, Hayek, and Keynes. In con-temporary usage, “rational” really means “model-consistent” expecta-tions under quantifiable risk—nonsense from anything but a particularepistemological point of view. For the new Austrians, incomplete knowl-edge à la Hayek is replaced by (nearly) perfect prescience in support of awelfare-optimizing economic system which seeks its ends independent ofpolicy moves.4

Third, as Mirowski (2002) argues, after World War II there was a con-certed effort, with the Cowles Commission, MIT, and (to a degree) Chi-cago in the vanguard, to mathematize microeconomics in support ofWalrasian models and subsequently Nash equilibrium game theory (inMirowski’s view the Mephisto who provoked this campaign was noneother than the “Hungarian wizard” or mathematical “demigod” Johnvon Neumann). On this account, related developments in macroeco-nomics such as the neoclassical synthesis and new classical and newKeynesian modeling were automatic by-products because they could sellthemselves as being analytically high tech.

The new tricks included Lucas’s importation of the rational expecta-tions idea from the microeconomics of commodity markets, and exten-sive new classical use of the deterministic and stochastic optimal controlmethodologies being perfected by applied mathematicians in the 1960s.The notion that there is a “true” model of the economy may have comefrom this source.

After all, if optimal control models building on Newton’s (true) lawsenable NASA to guide a rocket to the moon under statistically noisy con-ditions, why can’t stochastic optimization analysis also be applied to an“islands” economy for which we are assured a unique model exists? Thedifference is that when in 1684 Edmund Halley (of later comet fame)

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went up from London to Cambridge to ask the celebrated but some-what strange mathematician Isaac Newton to clarify the rumors thatwere running around about inverse square gravity laws, he got the defin-itive answer in the form of Principia Mathematica within three years;Walrasian economists have not produced anything remotely comparablein over one hundred. The economy rests on changing social relations—all attempts to describe it in terms of timeless constructs like Newton’slaws, Einstein’s field equations, or Feynman’s diagrams are bound to fail.Stochastic but rational expectations built upon a nonexistent “true”model correspondingly have no content.

Finally, the alleged intellectual power of the new techniques was but-tressed by the convenient “collapse” of the empirical Phillips curve in thelate 1960s. The story is that Phillips (1958) found a century-long associ-ation in the United Kingdom between changes in unemployment andwage inflation. Samuelson and Solow (1960) observed a seemingly simi-lar inverse correlation between price inflation and the unemploymentrate in post-Depression U.S. data. This relationship continued to fit thenumbers well until around 1970, when inflation accelerated while unem-ployment rose in a burst of “stagflation.” This breakdown of the Phillipsrelationship left the gates of macroeconomics wide open for anti-Keynesian theories to charge in.

With hindsight and in terms of structuralist inflation theory, the eventsof the 1970s are not so startling. We now know that the institu-tional consensus which supported the historically unprecedented outputgrowth rates of the Golden Age between the late 1940s and the late1960s had fallen apart, with worldwide reductions in productivitygrowth and capital accumulation (Glyn et al. 1990). Conflict was on therise, spilling over into faster inflation and social unrest. As will be shownin Chapters 7 and 9, wage and price inflation and their expectations in-teract in complicated fashion. An upward shift in pressure for wage in-creases together with downward movements of productivity growth andthe investment demand function provide the basis for a coherent, so-cially based theory about events in the 1970s that is verified herein andelsewhere (see Bowles, Gordon, and Weisskopf, 1990, for example).

Even with the Samuelson-Solow period included, longer-term data forindustrialized economies on inflation versus the rate of employment orcapacity utilization such as those presented by Galbraith and Darity(1994) and Romer (2001) typically show up as a cloud of points in the(u, ¾) plane, perhaps with a gentle inclination from southwest to north-east. One interpretation is that ¾ on the vertical axis is the “dependent”variable driven in the long term by u and its determining factors on thehorizontal. The most obvious statistical association is a line with a slightpositive slope (“the” Phillips curve) or maybe a curve that undulates as

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in Figure 7.1 below in Eisner’s (1996) tentative interpretation. One im-plication is that the unemployment cost of policies aimed at substantiallyreducing inflation is likely to be high.

Were u the “dependent” variable, the regression line through the datacloud would be near-vertical (instead of near-horizontal) with an inter-cept not far to the left of u’s sample mean. This is the “vertical Phillipscurve” at the heart of monetarist and new classical models. The datathemselves no more point toward a vertical curve than a flat one; thecausal structure to be imposed on the numbers has to come from out-side the (u, ¾) plane. Monetarists and new classicists happen to prefer aWalrasian interpretation in which u responds to price changes (plus ran-dom error terms) but is basically fixed;5 structuralists see ¾ as respondingto u in a fairly complicated system which may include feedbacks such asthe inflation tax and forced saving.

Friedman, Lucas, and friends would have painted their preferredmodel on the data regardless of whether the American Phillips curve had“collapsed” or not, but there is no denying that the break in Samuelsonand Solow’s phenomenological relationship came at just the right time togive anti-Keynesian arguments tremendous polemical force.

2. A Chicago Monetarist Model

In stripped-down form, both monetarist and new classical models can bedescribed in three equations. In the (u, ω) plane used throughout thisbook, there is a reduced form aggregate demand relationship which canbe written as

ua = f a(γg, M/P), (1)

where γg is the fiscal deficit (scaled by the capital stock) and M/P standsfor real money balances.

In Friedman’s version of the model, labor is demanded by firms whichcan perfectly observe the product wage ω = w/P. By Keynes’s first classi-cal postulate, the number of people they employ and therefore the levelof economic activity ud will be an inverse function of ω along an f d sched-ule which combines a “production function” relationship between ud

and the labor/capital ratio λ, and a “labor demand” relationship be-tween λ and ω (recall the hat calculus discussion in Chapter 2):

ud = f d(ω). (2)

Finally, workers rely on out-of-date price information, because eitherthere are lags in contracts, it is not easy to gather information on a bigset of prices to recalculate the consumption wage continuously, or it

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takes time for price data to diffuse across Phelps’s islands. The labor sup-ply decision is thereby based on an expected price Pe. If we let ξp = P/Pe,labor supply will depend on w/Pe = ωξp. Running this response throughthe production function gives

us = f s(ωξp). (3)

In many presentations of the accelerationist model, (3) is treated as a“notional” relationship with macro equilibrium being determined by (1)and (2). An upward shift in aggregate demand (from a higher moneysupply M, say) would shift the ua schedule to the right from an initialpoint A, as in Figure 6.1. The new short-run equilibrium would be atB, ratified by a lower real wage ω. Presumably the reduction in ω isachieved by a jump in the price level P, which also would shift the ua

schedule back toward the left. Workers aren’t quite with it because theythink the real wage is still ωξp at the “old” level of ω. But with a lag theyrevise expectations according to an error-correction rule such as

Óp = ρp(1 − ξp), (4)

and the us schedule begins to shift downward.The story doesn’t end there, however. Workers are getting paid a real

wage lower than they want so long as the value of ω along the us curvelies above its value at the intersection of ua and ud; they may start push-ing for higher money wages as a consequence. The price level will re-

204 chapter six

Real wageω

Output/capitalratio u

A

B

ua

us p( )ϖξ

ud( )ϖ

Figure 6.1Standard diagram forthe Friedman-Phelpsmodel.

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spond through producers’ cost functions, pushing the ua curve furtherback to the left via the real balance effect. After some sort of dynamicprocess, the economy will end up again at point A, with the demandjump eroded by higher prices and Say’s Law in force. This “policy neu-trality” result is the central thrust of both monetarist and new classicalanalysis; it just takes a while to work itself through in the Chicagoversion.

3. A Cleaner Version of Monetarism

The foregoing narrative is all right as far as it goes, but it leaves the de-tails of dynamic adjustment a bit fuzzy. The plot can be clarified if westick with Say’s Law, but assume fast adjustment of both nominal vari-ables P and w. Such a use of separate market-clearing equations forprices and wages is characteristic of recent structuralist models such asthose in Flaschel, Franke, and Semmler (1997).

The price level naturally varies to clear the commodity market,

f a(γg, M/P) − f d(w/P) = 0. (5)

That is, an increase in P reduces aggregate demand via the real balanceeffect and raises output because firms hire more workers.

A higher money wage w clears the labor market,

f d(w/P) − f s(w/Pe) = 0, (6)

by reducing labor demand and increasing supply.Workers’ adaptive expectations in (3) can be rewritten as

¾e = ¾ + ρp[(P − Pe)/P], (7)

where ρp again is a response coefficient. Equations (5)–(7) make up acomplete dynamic model.

The first two relationships can be analyzed using comparative statics.Their behavior in the short run can be illustrated if we use hat calculus torewrite them in log-linear form,

aÒg + b(þ − ¾) + c(œ − ¾) = 0 (5′)

and

−c(œ − ¾) − d(œ − ¾e) = 0, (6′)

where a, b, c, and d are all elasticities. Restating these equations in ma-trix notation gives

− +− +

( )( )

b c cc c d

¾$w− +

−( )αÒg

e

bd

þ¾

(8)

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Because (b + c)/c > 1 > c/(c + d), the slope d(log w)/d(log P) of theCommodity market schedule is greater than one, and the slope of the La-bor market curve is less than one, as shown in Figure 6.2. A shift to theright of the commodity schedule induced by Òg > 0 or þ > 0 increasesthe P/w ratio, or the real wage falls. An upward shift in the labor marketlocus when ¾e > 0 increases w/P.

With this information at hand, we can quickly run through a couple ofadjustment scenarios, beginning at an initial equilibrium where Pe = P.As just noted, a higher γg makes P jump up more than w, leading firms tohire more workers and output to increase. From (7), Pe begins to rise,pushing up w and P with less than unit elasticities (as is easily verifiedfrom the algebra in (8)) but raising w/P. Aggregate demand ua declineswith the continuing increase in P, supply us falls back as w rises less thanP, and the output level ud corresponding to labor demand drops off witha higher w/P.

These three shifts together drive the system back to its initial outputlevel, but with higher nominal values of w, P, and Pe. Consumptiondemand is 100 percent crowded out by higher fiscal spending through areduction in real balances M/P. There is a similar long-run response toa jump in the money supply, except that after the adjustment is com-plete levels of government and private consumption remain the same.In the short run, monetary stimulus may be effective through thePigou/Patinkin and Keynes effects, but its long-term potency is nil. Be-

206 chapter six

45°

Money wagelog w

Price levellog P

Commoditymarket

Labormarket

Figure 6.2Nominal price andwage adjustment inthe Friedman-Phelpsmodel.

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cause in Friedman’s world the permanent income hypothesis makes de-mand multipliers vanish, fiscal policy is weak in both the short and thelong runs.

To summarize, we have a story in which the real balance effect makessure that Say’s Law holds in a static model. Price and wage increasesfully offset efforts at inducing higher employment by expansionary pol-icy. Contractionary policies would be symmetrically frustrated by priceand wage reductions. These exercises all take the form of comparativestatics, with no dynamic processes except changes over time of Pe. Afterall the uproar about overthrowing the Phillips curve, whatever has hap-pened to inflation?

The only way that ongoing price increases can be kindled in the pres-ent model is by persistent growth of the money supply, perhaps support-ing Friedman’s slogan that “inflation is always and everywhere a mone-tary phenomenon.” But with a lag of decades, his dynamics (implicitlybased on “helicopter drops” of currency) lack the institutional richnessof Wicksell’s. The liveliest story involves conscious acceleration of infla-tion by the authorities. With luck, they might keep employment above itsSay’s Law level for a time, thereby giving the model its “accelerationist”nickname. For all its enormous impact on politics and policy, the intel-lectual content of the monetarist counterrevolution is remarkably thin.6

4. New Classical Spins

The main difference between new classical macroeconomics and itsmonetarist progenitor is that it makes policy ineffectiveness propositionscome true instantaneously. The Lucas et al. model can be viewed as aspecial case of Friedman’s machine in which the adjustment coefficient ρp

in (7) goes to zero so that ¾e becomes very nearly equal to ¾. Equation (8)can be restated as

− ++ − +

( )( ) ( )

b c cc d c d

¾W$ = − +( )αÒg bþ

0 (9)

As shown in Figure 6.3, the Labor market schedule now coincideswith the 45o line. Expansionary policy in the form of a positive valueof Òg or þ will shift the Commodity market schedule rightward andimmediately increase w and P in equal proportion, so that real outputstays constant. Attempts at government intervention rapidly dissipateinto nominal price jumps up or down; in the jargon, policy “super-neutrality” reigns.

As noted in previous chapters, the assumption that ¾e = ¾ is not obvi-

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ously crazy. After all, people do learn rapidly about the state of play onthe inflation front. The more relevant questions are whether it makessense to use the real balance effect to suppress effective demand andreplace it with the second classical postulate, and whether it is more ap-propriate to pass a flat or steep summary line through the inflation rateversus activity level data cloud. People can have honest disagreementsabout the answers, no doubt linked to their political positions and socialpredilections. Only extremely careful scrutiny of the data combined withinstitutional and historical knowledge coming from beyond technicaleconomics per se can help to resolve them.

Such circumspection was not for the new classicists. Rather, on the ba-sis of their radical Austrian positivism they spelled out additional propo-sitions in support of Say’s Law. The best known is the Lucas (1972)“supply function,” which justifies dependence of u on ¾ (broadly inter-preted) rather than the reverse structuralist causality. In detail, the analy-sis involves symmetrical producers on Phelpsian islands, each specializedin selling a single product with price Pi and all consuming the same bas-ket of goods made up of products from the whole archipelago.

Demand for each good is subject to a random shock zj so that its salesvolume is Xi = X(Pi/P)−ηzi, where η is the price elasticity of demand (thesame for all goods),7 P is a consumption price deflator, and X is total realdemand obeying the quantity theory rule X = M/P. When equilibrium isattained and error terms average out, normalization “per island” will

208 chapter six

45°

Money wagelog w

Price levellog P

Commoditymarket

Labormarket

Figure 6.3Nominal price andwage adjustment inthe new classicalmodel.

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make Pi = P and Xi = X. The money supply M is also subject to randomshocks. Together with the zi, the shock to M makes observation of theprice index P subject to probabilistic errors or noise.

Up to its stochastic specification, this model has the same structure asthe ones discussed previously in this chapter. The first and second classi-cal postulates apply because each producer maximizes a function basedon utility from consumption and disutility from work, giving rise tocurves similar to the us and ud schedules, which shift with the zi. The X =M/P rule with M subject to random shocks has the same content as aschedule for ua. The error terms are the new elements.

Rational or model-consistent expectations enter when we assume thatall agents have complete knowledge of the technical details of produc-tion and consumption (the new classical “laws” of economics), and thatthey estimate P subject to known probability distributions for the zi andthe shock to M. Under strong behavioral assumptions—the main onesbeing that the island agents all share the same quadratic utility functionin logs of employment and consumption, and that there are Gaussianprobability distributions for log zi and the log of the shock to M—a log-linear supply rule emerges from this formulation (Romer (2001) gives aclear presentation of the manipulative details). Each agent will end upsupplying its product in accordance with an economy-wide equationthat can be written as

log X − log ² = b[log P − E(log P)]. (10)

Quadratic utility and Gaussian shocks together guarantee that log Xdepends in linear fashion only on E(log P) or the mathematical expecta-tion of the log of the overall price level and not on this random vari-able’s higher moments. According to Keynes, of course, even the ex-pected value has no meaning.

Equation (10) is the famous “surprise” supply function. Output willdiffer from its Walrasian level ² when log P randomly departs from itsexpected value. “Unexpected” price excursions or “inflation” explainsany observed deviation of output and employment from the “natural”levels which fix the position of the vertical Phillips curve.

This formulation is a methodological refinement of the “expectations-augmented Phillips curve” which emerged in the wake of Friedman andPhelps,

¾ = ¾e + a(log X − log ²) + ζ, (11)

where ² is the NAIRU output level at which ¾e = ¾ and ζ stands for sup-ply shocks. When estimated subject to a rule like (7) for formation of ex-

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pectations (not probabilistically expected values, necessarily) with ¾ asthe endogenous variable, equation (11) yields a small positive regressioncoefficient a, that is, a “horizontal” short-run Phillips curve. Because ¾e

is a linear combination of lagged values f(¾lag) of ¾, the change in infla-tion as measured by ¾ − f(¾lag) will be positive when X exceeds ².

This “accelerationist” interpretation is neat, but depends on econo-metric sleight-of-hand which gives the intercept of the regression equa-tion (11) the particular label −a(log X). Without this trick, (11) be-comes

¾ = A + ¾e + a(log X) + ζ, (12)

where A < 0 is an intercept term estimated in the usual way (scalinglog X around its sample mean will make A negative when a > 0).

As noted above, if a convergent process is postulated for ¾e, thenthe Phillips curve (12) turns out to be nearly flat, or possibly configuredlike a snake crawling gradually northeast in the (log X, ¾) plane. Insteady state, the effects of changes in log X on the inflation rate are smalland may be of uncertain sign. A vertical long-run Phillips relationshipemerges from (11) only when the intercept term A in (12) is said to definea NAIRU output point at which ¾e = ¾ and ζ = 0.

For new classicists, the Lucas model (10) rules out such undesirableoutcomes by reversing causality to make X a function of random shocksto log P, rather than having ¾ depend on X. If a in (11) or (12) is smalland positive, then its inverse b in (10) will be satisfyingly large. Log Xwill respond strongly to a shift in the variable [log P − E(log P)]≈ ¾ andthe Phillips curve will be nearly vertical. Such a robust short-run re-sponse of output and labor supply to price changes underlies the realbusiness cycle models discussed later in this chapter. Unfortunately forits proponents, a large b coefficient is not easily inferred from industrial-ized economy employment data.

Utilizing his supply function, Lucas (1976) launched a well-knowncritique of phenomenological constructs like the Samuelson-Solow Phil-lips curve. The basic story is that if the authorities speed up money-sup-ply growth to raise employment, this trick will work only so long as itdrives a “surprise” increase of log P in (10). More likely sooner thanlater, people will catch on and raise E(log P), driving X back to its natu-ral level where it belongs. Econometric estimates of the Phillips curveduring this transition process may look good, but really don’t mean any-thing.

The idea that the statistical relationship between X and ¾ may changeif policymakers attempt to take advantage of it became the mainstreamrationale for the acceleration in inflation observed in industrialized econ-

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omies in the 1970s. In the United States in particular, poor Lyndon John-son and his neoclassically synthesizing economic advisors just didn’trealize that the public would smoke out their efforts to drive the unem-ployment rate down and keep it there by pursuing monetary and fiscalexpansion (the Vietnam-related contribution to these policies was notanticipated by the advisors, but that’s another story).

As already discussed, from a structuralist perspective shifts in thefunctions underlying the model presented in Chapters 7 and 9 in associa-tion with observed social and political changes seem a less-contrivedexplanation for faster inflation in the 1970s. As a structuralist modelwould further predict, inflation then slowed after interest rates wereraised dramatically in 1979 and Ronald Reagan moved to break labormilitancy by firing the air traffic controllers in 1981 and to cut produc-tion costs by appreciating the real exchange rate. No endogenous shiftsin mathematically expected inflation rates need be postulated to explainobserved events. But to repeat a thought from Chapter 1, parsimony inexplanation in the sense of William of Occam rests in the eye of the be-holder.

5. Dynamics of Government Debt

Barro (1974) stars in the next episode in the new classical chronicle. Hekicked off an enormous debate about the “Ricardian equivalence” of taxand debt financing of government spending. The basic idea is that onlygovernment purchases and not the means by which they are financed af-fect the real side of the economy.8 The SAM in Table 6.1 leads into theargument. Its setup is similar to the one in Table 3.2, which we used toanalyze the Wicksell and (much more akin to Barro) Sargent-Wallace in-flation models.

To begin with the accounting, households receiving wage income holdthe debts Dg and Df of government and firms. The corresponding interestpayments (at the real rate j) show up as income flows in cells B3 and B4of the matrix, where δ = D/PK, β = Df/D, 1 − β= Dg/D, and Df + Dg =D. Other items of note include the entry τh in cell D2, representing lump-sum taxes on households (like all other variables in the matrix, τh isscaled by the value of the capital stock PK).

Household income is ξh = (1 − π)u + jδ. The corresponding sav-ing flow, σh = ξh − γh − τh, is used to acquire more debt δˆ = ©/PK inthe flow of funds row (E). In rows (F) and (G) firms and government is-sue new debt to cover their deficits g − σf = g + jβδ − πu and −σg = γg +j(1 − β)δ − τh respectively (profit flows remaining after interest pay-ments by firms are assumed to be saved). As usual, g = I/K is the growthrate of the capital stock.

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From row (A) of the SAM, we have

γh = u − γg − g. (13)

In the steady state of a neoclassical growth model of the Ramsey orSolow type g is predetermined by labor force growth (assuming that pro-ductivity growth is zero). The output/capital ratio u and profit share πwill be set by marginal productivity rules. For given values of u and g,equation (13) shows that if government spending γg goes up, then house-hold consumption γh has to be crowded out 100 percent, regardless ofwhether the extra public spending is paid for by higher taxes or issuingmore debt. Moreover, with γh as an endogenous variable in cell A2 andthe tax burden τh determined by policy in cell D2, household saving σh

must be endogenous in cell E2. The relationship

σh = (g − πu) + (γg − τh) + jδ (14)

can be derived from the SAM accounting. The saving/capital ratio σh hasto move to cover financial deficits arising in other sectors as well as totalinterest payments jδ.

These tautologies of accountancy are the basic Ricardian equivalenceresults, with the key element being the endogenous adjustment of σh in(14) to offset changes in the tax and debt variables τh and jδ for a givenγg. If taxes go down, then σh goes up in equal measure, “in anticipation”of the inevitably increased fiscal debt burden to come. Barro offers a ra-tionale for the endogeneity of σh in a Ramsey model, but before we get

212 chapter six

Table 6.1 A SAM incorporating government debt and taxes (all variables scaled by the value of capital stock).

Current expendituresLoans to firms& government TotalsOutput costs Households Firms Government Investment

(1) (2) (3) (4) (5) (6) (7)

(A) Output uses γh γg g uIncomes(B) Households (1 − π)u jβδ j(1 − β)δ ξh

(C) Firms πu ξf

(D) Government τh ξg

Flows of funds(E) Household σh −δ $D 0(F) Firms σf −g βδ $Df 0(G) Government σg (1 − β)δ $Dg 0(H) Totals u ξh ξf ξg 0 0

Definitionsδ = D/PKβ = Df /D1 − β = Dg /D

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into that it makes sense to explore debt dynamics without household op-timization.9

The key equation for the increase of δ = D/PK follows from substitu-tions within the SAM. It is

â = (g − πu) + (γg − τh) − (g − j)δ. (15)

The state (or ratio) variable δ goes up with the “primary” deficits g − πuand γg − τh of firms and the government respectively. It is self-stabilizingwith dâ/dδ < 0 when g > j, or the rate of growth of output exceeds thereal rate of interest.10 The economy can “grow out” of the burden ofdebt if the g > j condition is satisfied. Note the similarity to the profitrate > population growth rate condition for stability of the Keynesianfully funded pension model toward the end of Chapter 5. In both cases, a“growth factor” has to exceed a “leakage factor” for the dynamics to bestable.

When the g > j condition holds, setting â = 0 in (15) shows that thesteady-state ratio of debt to capital is11

δ = [(g − πu) + (γg − τh)]/(g − j). (16)

In words, the debt ratio settles down to the sum of business and govern-ment primary deficits as scaled to the value of capital stock, capitalizedby the difference between the growth and real interest rates. In realworld markets, national “solvency” can become worrisome when thedebt/GDP ratio exceeds, say, 100 percent. A critical value for δ therebymight be in the vicinity of one-third.

Even with the steady-state hypothesis ˆ = g (or a constant δ alongwith a constant P) imposed on the accounting in Table 8.1, the real inter-est rate j remains undetermined. A traditional fiscal economist might usethis degree of freedom to introduce a saving function of the form

σh(j) = δˆ, (17)

adding behavioral content to SAM row (E).In the standard scenario, the total primary deficit Q of firms and gov-

ernment is positive: Q = (g − πu) + (γg − τh) > 0. The steady-state equa-tion (16) can be rewritten as

j = g − (Q/δ), (16′)

which becomes the Debt schedule in Figure 6.4. Along this curve, the in-terest rate is zero when δ = Q/g, and rises asymptotically to the level g asδ goes to infinity.

The Saving schedule represents (17) in steady state. As drawn, it cutsthe debt locus twice, with a stable equilibrium at A and an unstable one

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at B. Suppose that the economy is initially at A, but that the governmentchooses “permanently” to increase its primary deficit γg − τh. This policychange will make Q go up, shifting the intercept of the Debt curve on thehorizontal axis to the right and raising the steady-state values of δ and j.From (17), the increase in j will call forth more household saving tofinance the government’s bigger deficit and cut household consumptionto satisfy the accounting restrictions (13) and (14). In a Keynesian for-mulation as in Chapter 4, a higher interest rate would also reduce invest-ment demand and the growth rate gi. The intercept Q/gi of the debtschedule would shift further to the right, in a potentially destabilizingfeedback.

If the government further pursues its profligate ways, the Debt sched-ule may shift far enough to the right not to intersect with the savingcurve. Then the economy will fall into a true debt trap, with j and δ bothdiverging toward infinity until someone on horseback canters in andstraightens out the fiscal mess.

6. Ricardian Equivalence

This last scenario is the stock-in-trade of old-fashioned fiscal conserva-tives, who exist all across the political spectrum. In India, for example,the Left traditionally raises the specter of an imminent debt trap. In the

214 chapter six

Real interestrate j

Debt/capital ratioδ = D/PK

A

B

Saving

Debt

g

Q/g

Figure 6.4Debt dynamics in atraditional model.

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United States, the main official rationale for the tight fiscal policy of theClinton administration was its alleged effectiveness in holding interestrates down (even though in the late 1990s real long rates were at all-timehighs). Sometimes such notions are not off the mark, as is their labormarket analog illustrated in Figure 2.7 and even the inflation tax Laffercurve in Figure 3.8. But Barro is after bigger game. He wants to show notthat the government is capable of fiscal (ir)responsibility, but that how itfinances its excesses really doesn’t matter, a cheering thought for Ameri-can conservatives like the writers for the editorial page of the Wall StreetJournal during the times of Ronald Reagan’s (and more recently GeorgeW. Bush’s) exploding public deficits. Regardless of how it is paid for, allthat government expenditure can do along an optimal growth model iscrowd out (worthy?) private consumption.

Barro consolidates the households and firms of Table 6.1 into a pri-vate sector, and normalizes variables by the fully employed labor force Las opposed to the capital stock PK. The corresponding SAM appears inTable 6.2, with x = X/L, k = K/L, gk = (I/K)(K/L) = I/L, ∆ = D/L, andso on. Row (A) can be rewritten as

cp = x − cg − gk, (18)

where cp and cg are private and government consumption per capita. Asin (13), there is 100 percent crowding-out of private by higher publicconsumption, because x and gk are fixed by Say’s Law and steady-stateassumptions.

monetarism and new classical macro 215

Table 6.2 Another SAM incorporating government debt and taxes (all variables scaled by labor supply).

Current expendituresLoans to

government TotalsOutput costs Private sector Government Investment(1) (2) (3) (4) (5) (6)

(A) Output uses cp cg gk xIncomes(B) Private sector x j∆ yp

(C) Government t yg

Flows of funds(D) Private sector sp −gk −∆ $D 0(E) Government sg ∆ $D 0(F) Totals x yp yg 0 0

Definitions∆ = D/Lx = X/Lk = K/L

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To reach full Ricardian equivalence whereby the government’s shiftsbetween tax and debt financing are offset by shifts in private saving, twosteps are required. The first is to cut links between debt dynamics andchanges in the interest rate such as those discussed in section 5. The sec-ond is to avoid debt traps. In a mode of argument dear to all economists,new classicists take both strides by making the appropriate assumptions.

They begin by postulating that household saving decisions followfrom a Ramsey model like the one discussed in Chapter 3, with Eulerequations of the form

| = f(k) − cp − cg − nk (19)

and

˜p = (cp/η)(f′ − À), (20)

where n is the rate of population growth (in steady state, g = I/K = n), ηis the elasticity of the marginal “felicity” of consumption, and À is a purerate of private time preference.

Recall from Chapter 3 that for a solution to the Ramsey problem toexist, the condition À > n is required, that is, the discount rate has to ex-ceed the rate of population growth. At a steady state with ˜p = 0, (20)shows that f′ = À, or the marginal product of capital equals the discountrate. Competition in the financial market will further ensure that the realinterest rate j equals f′. In line with most of the literature, we focus onthese steady-state results.

The equality between j and À is tricky, because manipulation of ac-counting balances in the Table 6.2 SAM shows that the debt/labor ratioevolves according to the rule

ß = (cg − t) − (n − j)∆, (21)

where t stands for lump-sum taxes per capita. With j = f′ = À > n thisequation is unstable with dß/d∆ > 0. How can the economy avoid adebt trap?

To lead up to an answer, we have to examine the stability of the wholesystem (19)–(21). Linearized around a steady state, its partial derivativematrix has the form

k cp ∆| À − n −1 0˜p (cp/η)f″ 0 0ß 0 0 À − n

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The zero entries in the last row and column show that debt dynamicsare delinked from k and cp—this is the first step toward Ricardian equiv-alence. As we have seen in Chapter 3, subject to enough transversalityconditions the differential equations for | and ˜p will “converge” to asaddlepoint steady state. The presence of cg in (19) makes sure that theaccounting balance (18) is satisfied. An argument like the one made inconnection with Figure 3.4 shows that if cg changes in (19), then cp will“jump” to bring the economy to a new steady state. Otherwise, k and cp

would go off on a divergent path.For a dedicated new classicist, adding one more potentially unstable

process to the already divergent Ramsey model (19) and (20) is not toworry: “[I]ndividuals who optimize over an infinite horizon would nothold public debt that grows asymptotically at a rate as high as the inter-est rate. . . . This condition rules out Ponzi games or chain letters wherethe government issues debt and finances the payments of interest andprincipal by perpetual issues of new debt” (Barro 1989, pp. 203–204).The omniscient market will force the government to keep its financesfrom blowing up. Ponzi games will be avoided if the state runs a primarysurplus t − cg > 0 to pay the interest required to keep the debt stock percapita at the level

∆ = (t − cg)/(À − n) (22)

that holds ß = 0 at the (unstable) steady state.Analogously to (14), the accounting relationships in Table 6.2 can be

used to show that private saving per capita sp at steady state will satisfythe equations

sp = (cg − t) + j∆ + nk = n(k + ∆), (23)

where it is assumed that j = À and the expression after the second equal-ity follows by substitution from (22). Saving adjusts to cover the expan-sion of capital and debt required to keep up with population growth,and the debt/labor ratio ∆ itself varies to offset tax and spendingchanges. If cg or t shifts in (23), then sp will jump to preserve the firstequality.

The biggest worry with all this, of course, is that infinite perfect fore-sight may falter. What if it fails to guide the economy to comply with allthe transversality conditions required at the end of time to offset dy-namic instability arising from the two positive eigenvalues of the system(19)–(21)? One might feel safer with an old-fashioned stability conditionsuch as a higher growth rate than interest rate. Barro, however, argues

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that such caution is misplaced. In an overlapping generations frame-work, “optimal” bequests will chain the decisions of mortals togetherover time to ensure that the steady-state conditions sketched here will besatisfied.

Before such a grand vision, objections such as the facts that purelump-sum taxes don’t exist and that most households face liquidity con-straints and do not optimize their saving decisions pale to insignificance.However, it is fair to say that Barro did not make the mainstream re-ally believe that the Reagan fiscal deficits were beside the point. In theClinton years, enough deficit hawks thinking along the lines of Figure6.4 survived to convince politicians that public spending should be cutand taxes (slightly) raised. Whether they or Barro along with newly re-surgent supply-siders and a few remaining pro-deficit Keynesians willcarry the day during the decade of the aughts is a question yet to be de-cided.

7. The Business Cycle Conundrum

Seemingly cyclical fluctuations of output and almost all other macrovariables are an enduring feature of advanced capitalist economies.Two different ways of thinking about these movements coexist uneas-ily in the current literature. One traces back to the late 1800s and foundits most influential form in the United States in the work of the Na-tional Bureau of Economic Research (NBER), in particular Burns andMitchell (1946) and Zarnowitz (1992). Thoroughly empirical, theNBER methodology concentrates on interconnections between phaseswithin one cycle and across cycles; the severity (amplitude) of cycles;and the co-movements of a wide range of economic indicators and activ-ities.

New classical economics is the foundation of more recent “real busi-ness cycle” (RBC) models, which in contrast to the NBER approachemphasize random as opposed to systematic behavior, ahistorical analy-sis in place of history-based discussion, and statistically independent se-quencing of phases and cycles instead of their interconnections. As dis-cussed in the following section, RBC models generate fluctuations withrandom shocks to an otherwise stable system; opposing scholars such asGoldstein (1996) see cycles as endogenous to capitalism.

A fundamental stylized fact for real business cycle models is that in theUnited States, for example, “detrended” real output demonstrates sig-nificant positive autocorrelations over short periods and weak negativeautocorrelations over longer ones. With trends removed by a moving av-

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erage, the quarterly time series for log GDP is tolerably well modeled bya two-period autoregression,

log GDPt = α(log GDPt−1) − β(log GDPt−2) + À, (24)

where α > β > 0 and À is the usual error term. The negative coefficienton the second lag generates the “hump-shaped” response to distur-bances which is typically observed (Blanchard and Quah 1989). Ofcourse, if log GDPt is highly correlated with log GDPt−1 (a truism), thenwith the double lag the computer is almost certain to come smiling backwith two oppositely signed “highly significant” coefficients which sumto a value close to the coefficient in the single-lag regression. How seri-ously one should take the hump emerging from this construction is anopen question.

Although we won’t go into the details until Chapter 9, models inwhich output is driven by effective demand can track the business cy-cle reasonably well. Variants include multiplier-accelerator formulationsstemming from Samuelson (1939) through distributional shifts inGoodwin (1951, 1967) and onto financial cycles as in Minsky (1975).Recent mainstream discussion has focused on how central bank inter-ventions to stem U.S. inflation tend to throw the economy into recession(a finding belied by Fed tightening in 1999–2000 unless what is termed“inflation” is extended from goods prices as discussed by Romer andRomer (1989) to asset prices as well). The cycle models presented inChapter 9 incorporate many of these themes.

8. Cycles from the Supply Side

Demand-driven cycles, however, do not completely dominate the discus-sion. In terms of the diagrams in Chapter 5, “counterclockwise” read-ings of macro causality from the supply side also have a long tradition inthe literature on price, employment, and output fluctuations.

On the left, the adverse cyclical effects of rising capital per worker—an increasing organic composition of capital—have long figured inMarxist discourse. On the Right, Wicksell and Austrian economists suchas von Hayek (1931) saw depressions as an essential antidote to an over-hang of excess investment resulting from banks’ holding the market in-terest rate below its “natural” level (the same “inefficiency” that cancrop up in the OLG models sketched in Chapter 3). This view underlaySchumpeter’s contemporary description to credulous Harvard under-graduates of the Great Depression as an unavoidable capitalist “cold

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douche” (Heilbroner 1999). In a clear extension of the entrepreneur-driven technical change in his Theory of Economic Development,Schumpeter grounded his own massive work on cycles on “waves” of in-novation, which could underlie output fluctuations ranging from periodsof a few years to grand fifty-year Kondratiev cycles.

Minus the marvelous political economy of his Capitalism, Socialism,and Democracy, Schumpeter’s (1947) temporally fluctuating technicalprogress has been picked up by the recent mainstream RBC school as thekey factor underlying output fluctuations. The formal models assumethat the level of output is determined by a neoclassical production func-tion with a multiplicative term for shifts in total factor productivity asdiscussed in Chapter 2, for example in period t, Xt = ztF(Kt, Lt), with zt

as the time-varying productivity term.The basic RBC trick is to assume that zt “this period” depends

strongly on its level zt−1 “last period” plus a current random error. Thestochastic term transforms the standard Ramsey model into a problemof dynamic optimization under risk—a nontrivial extension as discussedin section 9. With enough ad hoc assumptions imposed to give it aclosed-form solution, the stochastic Ramsey model cranks out a set ofstandard RBC results.

The first is that if there is a one-period lag between investment andcompleted capital formation, then the accounting is in place to makeoutput in period t depend on its levels in periods t − 1 and t − 2.12 Cun-ning choice of parameters enables such a model to replicate the hump-shaped two-period auto-regression of log output displayed in equation(24) above. Stadler (1994) reviews the best-known variants, beginningwith the original by Kydland and Prescott (1982). Most of the cyclicalaction comes from the productivity growth–forcing function. Just why zt

should fluctuate so vigorously (with a quarterly standard deviation of itsrandom shock term of about 1 percent in most applications) is neverfully explained.13

What about real wages and employment? As in the Ramsey andKaldor models discussed previously, under a full employment assump-tion, higher productivity automatically raises output per worker and thereal wage. Although the results are built in by the closure assumptions ofRBC models, their ability to generate pro-cyclical productivity and realwage movements is usually taken as a major point in their favor. Less en-thusiastically received has been their presumption that employment fluc-tuations over the cycle are due to labor/leisure substitution in responseto wage and interest (= profit) rate changes.

In detail, the “island” households making up the population are sup-posed to maximize a universally shared utility function with consump-

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tion and “leisure” as its arguments. A two-period optimization exerciselike the one discussed in connection with the overlapping generationsmodel in Chapter 3 makes labor supply in period t depend positively onthe real wage ωt and the expected interest rate rt+1 as in equation (33) be-low. The gist of the interest rate story is that with a high value of rt+1,working and saving the proceeds in period t becomes attractive in com-parison to working in period t + 1.

As discussed in section 4, strong employment responsiveness alongthese lines underlies the Lucas supply function. Facile labor/leisuretrade-offs also have to be built into RBC models if they are to replicatethe stylized fact that employment correlates positively with output in theUnited States over the cycle (remember Okun’s Law). Unfortunately forthe theory, microeconomic evidence like that presented by Ball (1990)suggests that changes in labor supply are quite insensitive to fluctuationsin real wages and interest rates.

The last criticism usually voiced by new Keynesian critics such asSummers (1986) and Mankiw (1989) is that RBC models ignore mone-tary disturbances as a major perturbation of aggregate demand. Inmaking this assertion, RBC people are true to their conservative men-tors Friedman and Lucas in treating output as being determined fromthe supply side. However, they go one step further in assuming “re-verse causality” in the equation of exchange: PX/V drives the “inside”(or commercial bank–generated component of) M in RBC models, ascredits and deposits rise to meet a higher transactions volume requiredby an increase in X. This tendency toward heterodoxy goes only sofar, however. RBC modelers ultimately need a nominal anchor to fixthe price level. They are much happier to find it in a predeterminedlevel of outside money than in a social process determining the moneywage.

Finally, beyond new Keynesianism there is a question about informa-tional and computational requirements implicit in models of how eco-nomic decisions get made. As noted above, RBC formulations boil downto a Ramsey model with a technological error term thrown in. Such exer-cises in dynamic optimization under quantifiable risk are extremely dif-ficult to solve if they do not incorporate special assumptions such as thequadratic preference functions and linear constraints which produce thesimple closed-form results discussed in connection with Lucas’s supplyfunction (10) and Hall’s “random walk” consumption model discussedin Chapter 4. Besides Lucas and Hall, they underlie the equity premiumpuzzle and the Modigliani-Miller theorem. Because such formulationsare pervasive, it makes sense to present a sketch of how they can be ana-lyzed and (possibly) solved.

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9. Optimal Behavior under Risk

Early RBC models were set up in discrete time, and we continue withthat convention here. In intuitive terms, continuous-time stochastic opti-mization is not difficult to follow, but the formal mathematics (Itô’slemma, Kolmogorov’s backward equation, Feynman-Kac integrals, andall the rest) can be a bit daunting.14 Thus the discrete-time RBC Ramseyproblem at hand is

max Vt(t = 0) = E[ βtt t

t

T

U C L( , )]10

−=

∑ (25)

subject to

Kt+1 = (1 − δ)Kt + ztF(Kt, Lt) − Ct (26)

and

E[K(T)] = K*. (27)

The notation E( ) stands for the probabilistic expectation operatorover the “known” distribution of the zt. The maximand Vt in generalvaries as a function of time, with its value depending on the date t atwhich optimization begins to take place. The parameter β < 1 is a dis-count factor, U is the maximizing agent’s “felicity” function based onconsumption Ct and “leisure” 1 − Lt (where the agent can provide oneunit of labor at most), and δ is a “radioactive” depreciation coefficientvia which a proportion δKt of the entering capital stock disappears ineach time period. This formulation mainly differs from (15) and (16) inChapter 3 by including the random error terms zt in (26), which force theagent to maximize expected utility in (25). The way the model works ismost easily illustrated if the planning problem is assumed to end at some“distant” future time T, when the expected capital stock should arrive atits balanced growth level K* (the presence of the stochastic terms meansthat the target cannot be hit exactly).

Recall from Chapter 3 how the nonstochastic Ramsey model can besolved numerically using a feedback control rule based on backward in-tegration of the differential equation for its costate variable (say, ξ) froma terminal condition ξ(T) coupled with forward integration of the statevariable K from an initial condition K(0), with optimal choice of the con-trol variable(s) at each point in time. This procedure is “local” or “openloop” in the jargon of control engineers (Bryson and Ho 1969). From agiven initial value K(0), it can find an optimal path to K* at time T. Sev-eral such “extremal” trajectories are illustrated in Figure 6.5, starting

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out from different levels of K(0). Each one is fully optimal because it sat-isfies the initial and terminal conditions of the Ramsey model’s two-point boundary value problem as well as the relevant Euler equations.

Along each extremal (in discrete time), the value of the maximandVt(Kt) in (25) will vary, in general depending on the time t and value ofthe state variable Kt at which it is evaluated. The dashed curves are con-tours of constant V, which need not be orthogonal to the capital stocktrajectories. In the diagram, one can imagine “sweeping” V backwardfrom contour to contour over time, picking out optimal values of K (andassociated control variables) along extremals, in a global “feedback” or“closed-loop” control environment. This procedure is the essence of“dynamic programming.” The contemporary version is due to the math-ematician Richard Bellman (1957), who built on the Hamilton-Jacobipartial differential equation of classical physics.

Bellman was the first to admit that dynamic programming is bedeviledby a “curse of dimensionality.” To solve a general problem, one has tocompute and store values of V and K over the entire state space. Withpersonal computers of the early twenty-first century, such a calculation isfeasible for a few state variables. Supercomputers can do far more, ofcourse, but can we safely assume that island-bound optimizing house-holds are equipped with such machines?15

Supercomputing power is needed, unfortunately, to do dynamic opti-mization under quantifiable risk. In terms of Figure 6.5, the presence ofstochastic shocks means that the state variable randomly jumps from

monetarism and new classical macro 223

Statevariable

K

Time0 T

Contours ofconstant V

K*

Figure 6.5Optimal dynamicpaths and contoursof the return functionin a stochasticRamsey problem.

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one extremal path to another. To compute expected values over all thesepaths as required by (25), the full backward sweep of the dynamic pro-gramming solution has to be worked out. Applied RBC modelers canand do throw in enough special assumptions to make their models solu-ble analytically or with simple computer routines. Problem solvers in thereal economic world are not likely to be so lucky.

It is still of interest to go through the formal details of what they aresupposed to do. Bellman’s “principle of optimality” states that the back-ward sweep of the return function Vt can be taken in steps, with optimaldecisions about the control variables (Ct and Lt, in the present case)made during each one. This “recursive” principle boils down to findingVt (for successively lower values of t) according to the rule

Vt(Kt) = max,Ct Lt

U(Ct, 1 − Lt) + βE[Vt+1(Kt+1)], (28)

subject to the stochastic difference equation (26) tying Kt+1 to Ct and Lt.The backward sweep begins at time T with VT computed on the basis ofterminal or transversality conditions as sketched in Chapter 3.

Let UC,t and UL,t stand for the (positive) partial derivatives of the felic-ity function with respect to Ct and (1 − Lt) at time t, and let FK,t and FL,t

be the partials of the production function. Also, let Vt¢ be the derivativeof Vt with respect to Kt. Plugging (26) into (28) and maximizing with re-spect to Ct and Lt gives the rules

UC,t − βE(Vt+1¢ ) = 0 (29)

and

−UL,t + βE[Vt+1¢ (ztFL,t)] = 0. (30)

Also, in light of the envelope theorem, differentiating both sides of (28)with (26) substituted in (after Ct and Lt are optimized) with respect to Kt

gives

Vt¢ = βEVt+1¢ [ztFK,t + (1 − δ)]. (31)

This formula is a discrete-time, stochastic analog of the “backward”equation for the costate variable of the nonstochastic Ramsey model dis-cussed above, with V′ taking the role of ξ.16 In light of (29), one can re-place βE(Vt+1¢ ) by the nonstochastic variable UC,t in (31) to get

Vt¢ = UC,tE[ztFK,t + (1 − δ)].

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Changing the time subscript from t to t + 1 and substituting back into(29) gives the expression

UC,t = βE[UC,t+1][zt+1FK,t+1 + (1 − δ)] (32)

to determine consumption at time t.Equation (32) is a Ramsey-type optimal consumption rule (its contin-

uous-time, nonstochastic analog is equation (20) above). To see how itworks, suppose that the agent slightly reduces Ct, leading to capital accu-mulation and a higher expected value of output in period t + 1. The leftside of (32) gives the utility loss from this maneuver; the right side givesthe expected discounted utility gain from more consumption next pe-riod. At the margin, these expected costs and benefits should be equal.

The expectation in (31) is taken over the product of the stochasticvariables UC,t+1 and zt+1FK,t+1 + (1 − δ). By definition, for random vari-ables X and Y, E(XY) = E(X)E(Y) + cov(X, Y), where cov(X, Y) is thecovariance of the two. Suppose, for example, that consumption is highwhen the marginal product of capital is high. Then the covariance ofUC,t+1 and zt+1FK,t+1 + (1 − δ) will be negative, because marginal utility isan inverse function of Ct. The resulting low value of the right side of (32)means that UC,t will also be low. In other words, Ct will be optimized at ahigher value than would be the case if the covariance were zero. Pro-cy-clical variation of consumption and the rate of profit should be associ-ated with lower saving overall (a proposition difficult to test in practice,insofar as most saving is done by enterprises and their profit share movespro-cyclically).

One can go through similar manipulations to show that the agent’s la-bor supply rule takes the form

UL,t = UC,tE(ztFL,t). (33)

Marginal utility of leisure UL,t is a decreasing function of (1 − Lt). Hencea higher expected marginal product of labor (or real wage) E(ztFL,t) callsforth a higher level of work Lt. Similarly, from (32) a higher expected fu-ture marginal product of capital (or profit rate) makes UC,t and therebyLt rise in (33). These are the elastic labor supply responses of RBC mod-els discussed in section 8.

In practice, model builders in the RBC world usually impose enoughassumptions to make their dynamic programming problems soluble inclosed form. For example, McCallum (1989) shows that in the modeldiscussed here, Cobb-Douglas production and utility functions, purelycirculating capital (or δ = 1), and a log-normal productivity error term

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will do the trick. How well such a “tractable” specialization of themodel reflects its general pattern of results is not made clear.

10. Random Walk, Equity Premium, and the Modigliani-Miller Theorem

As pointed out at the end of section 8, stochastic dynamic programmingalso provides derivations of the random walk consumption model, theequity premium puzzle, and the Modigliani-Miller Theorem. We canquickly run through the mechanics here.

The random walk follows directly from (32) when accumulation forperiod t + 1 is not considered (FK,t+1 = δ = 0), and there is no discount-ing of the future (β = 1). The equation reduces to

UC,t = E(UC,t+1),

or

UC,t = UC,t+1 + ˢt+1 ,

where À¢t+1 is a “white noise” error term. Further, if the felicity function Uis quadratic in the variable Ct, we get UC,t = aCt, where a is a coefficient.The equation for optimal consumption choice becomes

aCt = aCt+1 + et+1¢ ,

which can be rewritten as

Ct+1 − Ct = Àt,

where Àt is also white noise. This equation describes the optimizing con-sumer’s drunkard’s walk.

The equity premium puzzle can be illustrated if we rewrite (32) as

UC,t = βE[UC,t+1(1 + rt+1)], (34)

where rt+1 is the stochastic return (net of depreciation) from engaging inproduction activity in period t + 1. Now contrast two firms, which havereturns positively and negatively correlated with UC,t+1 respectively. Thefirst firm is worth more because owning it allows the investor to hedgeagainst low values of Ct+1, which are associated with high values ofUC,t+1. The implication is that the first firm can pay a lower return thanthe second one to its owners. This logic underlies the popular capital as-set pricing model (or CAPM), which states that the higher the correla-

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tion of a firm’s returns with overall returns on the market, then thehigher the equilibrium yield on its stock has to be.17

The equity premium puzzle follows from (34), when one observes thatequity yields have a small positive correlation with C, or a small negativecorrelation with UC. Equity should therefore have to pay only a smallpremium over the return to riskless assets, nothing like the 5–6 percenthistorically observed in the U.S. market.

Equation (34) can be further tied into individual optimizing behavior,if the “investor” behind it is deciding whether to take over ownership ofa firm with value Zt and cash flow πt (where πt is profits net of invest-ment expenditure).18 The return to ownership becomes 1 + rt = (Zt+1 +π+1t)/Zt. Substituting into (34) gives

UC,t = βEUC,t+1[(Zt+1 + πt+1)/Zt]. (35)

The Modigliani-Miller theorem is implicit in this formula, which in ef-fect generalizes Irving Fisher’s theory of real returns to asset ownershipover wide domains of securities, agents, spaces of probabilistically ex-pected events, and time. To extract the theorem, we can follow Lucas(1978) and multiply both sides of (35) by the nonstochastic variable(Zt/UC,t) to get the difference equation

Zt = βE[(Uc,t+1/UC,t)(Zt+1 + πt+1)] (36)

in Zt and its expected future values. Because she has already workedthrough the relevant backward dynamic programming sweep (calculat-ing optimal expected consumption levels along the way), it is no greattask for the investor to solve (36) forward in time along the relevantextremals and let T go to infinity to get the expression,19

Zt = E[ ( / ) ],, ,β πsC t s C t t s

s

U U+ +

=

∑1

(37)

where expectations are taken sequentially over information available attime s. The worth of the firm is a fancy discounted present value of its ex-pected returns, with a time-varying discount rate depending on the in-vestor’s expected future levels of marginal utility.

To get rid of the marginal utility terms, it is conventionally assumedthat the existing set of securities “spans” all “states of nature” (indexedby n).20 Then all investors will equate their discounted marginal utilitiesin (37) to asset prices pn,t+s which give the values of “goods and securi-

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ties” in state of nature n at time t + s, relative to their prices in period t.That is,

pn,t+s = qn,t+sβsUC,t+s/UC,t,

where qn,t+s is the probability that state n will occur at time t + s. InLucas’s well-informed world, the qn,t+s must be interpreted as objectiveprobabilities, known to all agents.

Substituting the state-contingent prices pn,t+s into (37) gives

Zt = pn t s n t s

n

N

s

, ,+ +

==

∑∑ π11

, (38)

where the (finite?, countable?) number of states of nature is N.The Modigliani-Miller theorem basically says that given all the opti-

mizations and contingency-spanning securities we have postulated, itdoesn’t really matter how a firm chooses to package its ownershipclaims. In other words, the structure of its offering of securities is ir-relevant.21 In line with the arbitrage arguments underlying the theo-rem (sketched in the following section), suppose that a firm arbi-trarily divides its cash flows into stream E (“equity”) and stream B(“bonds”) with πn,t = πE,n,t + πB,n,t. If we expand upon (38), the value ofeach stream is

Zi,t = p i E Bn t s i n t s

n

N

s

, , , , , ,+ +

==

=∑∑ π11

(39)

with ZE,t + ZB,t = Zt. The algebraic linearity of all these manipulationsmeans that the firm’s value Zt does not depend on the labels it attaches toits securities. If, for example, it substitutes cheaper debt for equity, thenas in Figure 6.6 below it has to pay a higher return on equity because itsleverage has gone up.

The key assumptions are that the firm has zero net worth and that itstotal cash flows π are independent of their allocation into the boxes πE

and πB. Modifications to the latter assumption such as the fact that onlydividends and not interest payments are taxed at the corporate level(more bond finance increases π) and that greater leverage may drive upbankruptcy risk (reducing π) do not alter the argument’s basic thrust.

11. More on Modigliani-Miller

Because the foregoing discussion is rather abstract, it makes sense to tryto add some intuitive flesh to the algebraic bones. One way to do this isvia Modigliani and Miller’s original approach to their famous results.22

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Another gloss on the theorem is that if all of a firm’s publicly tradedsecurities exhaust the value of its assets, then the returns imputed tothese obligations exhaust all profits. The proof relies on argumentsabout gains from arbitrage that characterize much neoclassical thoughtand are implicit in the discussion of last section. Modigliani and Miller(1958) worked with firms 1 and 2, which both have an expected annualfuture profit flow Π. Their market valuations Z1 and Z2 should then sat-isfy the relationships Z1 = Z2 = Z = Π/ρ, where Π/ρ is their capitalizedreturn at the rate ρ appropriate to their “risk class” (loosely defined as agroup of firms with highly correlated returns).

The argument proceeds by contradiction, on the maintained hypothe-sis that both enterprises have zero net worth. Suppose that firm 1 issuesonly equity (Z1 = E1, where E1 is the value of its shares outstanding) andthat firm 2 is “leveraged” or “geared” because it issues both equity andbonds (Z2 = E2 + B2). What happens if Z2 > Z1?

The holder of a portion α of firm 2’s outstanding equity E2 gets a totalreturn Y2 = α(Π− jbB2), where jb is the ruling real interest rate on bonds.If there is a perfect capital market, he can sell his shares and also borrowthe amount αB2 to buy a fraction α(E2 + B2)/E1 of firm 1’s equity, usinghis new share holdings as collateral for the loan. The return Y1 to thisnew portfolio turns out to be

Y1 = α[(E2 + B2)/E1]Π − αjbB2 = α(Z2/Z1)Π − αjbB2.

That is, Z2 > Z1 means that Y1 > Y2. It makes sense to sell off E2 so thatZ2 declines and buy E1 so that Z1 rises, until Z1 = Z2.

Similarly, if Z1 > Z2, an owner of a portion α of firm one (with totalreturn αΠ) can sell off her shares E1 and buy a new portfolio made upof firm 2’s securities in the proportions E2/Z2 for shares and B2/Z2 forbonds. It is easy to show that the return to this portfolio is α(Z1/Z2)Π,which is higher than the original return αΠ when Z1 > Z2. The investor“undoes” firm 2’s gearing, to get access to its underlying valuation Π/ρ.

These arguments imply that the value of a firm is independent ofits financial structure. A similar statement applies to returns. If je is thereal rate of return to holding equity, then “return exhaustion” impliesthat Π= jeE + jbB. Because Π= ρZ and Z = B + E, this equation can berestated as

je = ρ + (ρ − jb)(B/E), (40)

which is illustrated in Figure 6.6. The “required” return to equity in-creases linearly with the firm’s debt/equity ratio B/E, perhaps tailing off abit (dashed line) if the cost of borrowing goes up with increasing lender’s

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risk when B/E is high. A relationship like (40) does not fit the observeddata badly.

Now the caveats. As noted above, the standard literature points outthat if debt and equity claims are taxed differently and/or if there is riskof bankruptcy, asset-holders may not be indifferent to a firm’s financialstructure. To these factors, one can add all the forces underlying differ-entiated borrowers’ and lenders’ risks as discussed in Chapter 4.

Finally, problems can arise in general equilibrium. Intuitively, the the-orem says that if a firm reduces its B/E ratio, then from (40) new equityowners will experience a reduction in their return stream. If asset-hold-ers can borrow and lend on the same terms as firms, they can buy or sellfinancial assets to offset the change. But for the arguments above to gothrough in general equilibrium, all owners of securities have to adjusttheir portfolios. If, for whatever reason, some do not do so, then thebond market will fail to clear and asset prices will have to change. Simul-taneous actions by all market participants are required to give the resultthat the financial structure of the firm is irrelevant.

12. The Calculation Debate and Super-Rational Economics

Maybe the best way to round out this chapter is to recall the outcome ofthe “calculation debate” of the 1920s and 1930s about the feasibility ofsocialist planning. The Left was represented by, among others, Lange

230 chapter six

Return toequity

je

Debt/equity ratioB/E

p

Figure 6.6The return to equityas a function ofdebt/equity ratio.

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(1936–37) and Lerner (1936), who argued that if the economy behavesin proper Walrasian fashion, then by controlling relative prices intelli-gently, a planner can guide the system to an efficient allocation of re-sources. In other words, central planning can work.

Scholars on the right such as von Mises (1935) asserted that planningwas bound to fail. “As if” socialist planners would merely “play” a mar-ket game, because they would not be disciplined by bankruptcy for mak-ing mistakes. Moreover, even if not misguided by such “agency” prob-lems, planners could not possibly get all their calculations right. If theybungled even a few key price relationships, especially those feeding intothe profitability calculus underlying investment decisions, they couldbadly upset production.

In retrospect, the Right appears to have won the debate—at least theSoviet version of socialism did not work out. The irony is that their intel-lectual heirs discussed in this chapter basically accept the Lange-Lernerargument that “really existing” capitalism is based on the actions of per-fect optimizers. Hence there is no need for the state to intervene to guidethe market’s behavior, and indeed any attempts at intervention will becounterproductive.

But what if merely mortal and fallible financiers and businessmenmake mistakes? Traditionalist Austrian economists believe that entre-preneurship in the market can overcome such “random shocks” whilenew classicists say they fit painlessly into agents’ exercises in dynamicstochastic optimization. If both are wrong—if history, institutions, andsocioeconomic structures matter in determining market outcomes—thenthe new Right’s vision of capitalism in the social order will turn out to beas misleading as was the Left’s optimism about the possibilities for so-cialism in the market.

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chapter seven

z

Effective Demand and theDistributive Curve

Chapters 7–10 cover recent ideas in structuralist macroeconomics—output determination, inflation, and distribution in this chapter, thenmoney and finance (mainly from a post-Keynesian perspective), cycles,and open economy issues with an emphasis on the exchange rate. In a bitmore detail, this chapter describes how determination of output andgrowth by effective demand interacts with the dynamics of distribution,inflation, and labor productivity growth emerging from market, insti-tutional, and social forces. Attention is paid to the effects of expan-sionary policies, and how they may affect distribution by changing in-come shares and shifting real returns to financial assets. We begin withdistribution, productivity growth, and inflation. Relationships betweensuch “supply” factors and demand are then illustrated with examples:the differential effects of faster productivity growth in profit- and wage-led economies; possibilities for implementing expansionary policy inprofit-led economies (without and then with financial repercussions);and three-way distributive conflicts in an economy open to foreign trade.

1. Initial Observations

Four introductory points are worth making. One is that social forcesset the rules via which nominal prices evolve. Money-wage dynamicsemerge from labor relations; commodity price and labor productivitygrowth depend on market power. In steady state, the rate of price infla-tion will equal the rate of wage inflation minus the rate of labor produc-tivity growth so that the real wage and productivity grow at the samerate and the labor share of output is constant.

Second, in confronting such a model with the data on any industrial-ized capitalist economy, some means has to be found to deal with thepresence of business cycles. An immediate question is: How does onecompare outcomes over cycles to steady states emerging from a growth/distribution model? For example, if real wages vary pro-cyclically, does

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that mean that the long-term average wage would be higher if the econ-omy could be managed in such a way as to maintain a higher averagelevel of capacity utilization? There is no way to answer such a questionapart from running the relevant experiment, but in historical time thatrarely happens. One common practice is to ground growth models onstylized facts extracted from cyclical behavior, and trust that their“trend” implications are valid. As will be seen, such an exercise can callfor fairly subtle interpretation of cyclical regularities. An alternative is tomodify steady-state models so that they can generate cyclical growth.The first approach is adopted in this and the next chapters, with modelsof cyclical growth following in Chapters 9 and 10.

The third observation is about the mechanisms via which the laborshare

ψ = wb/PX = ω/(X/L) (1)

and the level of economic activity u = X/K can combine to permit asteady state with a constant inflation rate and a stable income distribu-tion to exist. Under plausible assumptions, there is a curve in the (u, ψ)plane along which Ü = dψ/dt = 0 in steady state. A curve has a lot morepoints in it than the single (Ä, Ý) combination that defines a NAIRU asdescribed in Chapter 2; working in one dimension rather than zerovastly extends the range of macro policy combinations to be considered.Some possibilities are discussed in following sections, after we thinkthrough the details of a bare-bones structuralist analysis of distribution,productivity growth, and inflation.1

Finally, both the real wage and the productivity growth vary cyclicallyin the U.S. economy, meaning that dynamics of the wage share are drivenby changes in both ω and labor productivity ξL = 1/b = X/L. We discusssigns of wage, price, and productivity responses to shifts in ψ and u bydrawing upon cycle-based econometric results presented in Chapter 9,thereby illustrating the particular American case.

2. Inflation, Productivity Growth, and Distribution

Beginning with the social relationships built into the model, a first ques-tion is how to define an object of interaction between labor and capital.Because workers are concerned with their standard of living and enter-prises set prices as margins over costs, a complete formulation wouldwork with separate “consumption” and “product” wages (the moneywage deflated by the cost-of-living index and a relevant producer priceindex respectively), and also take into account nonwage production

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costs. To keep the algebra within bounds, these important details areomitted here (although section 8 does take up the implications of costs ofimported intermediate inputs). In the labor and commodity markets re-spectively, wage and price dynamics are assumed to be keyed just to thelabor share ψ, which does double duty as an indicator of worker/man-agement conflict and a measure of per unit labor costs.2 In keeping withthe literature, the analysis is phrased in terms of expectations about ψ,although this approach is more a convention than a contribution to in-tellectual clarity.

In the labor market, the models in previous chapters suggest thatworkers key their bargaining about the nominal wage to their expectedreal income share wb/Pe because they can observe the money wage theyreceive and how hard they are working, but (especially when computingthe cost-of-living index that determines their consumption wage) theycannot perfectly observe prices. If a higher wage share signals the pres-ence of enhanced worker bargaining power, one might expect wage in-flation to respond positively to an increase in wb/Pe. Greater resistanceto wage demands on the part of firms as the profit share erodes and unitlabor costs rise could give a negative response. From the econometrics inChapter 9, more rapid wage increases when ψ is high appear to be therule for the United States. There is also a weakly positive wage responseto u. The typical business cycle pattern is a falling (rising) wage share ascapacity utilization rises (falls) so that the two positive signs are consis-tent with a pro-cyclical nominal wage.3

Firms presumably make their pricing decisions in light of labor costsweb/P, where we is their expected money wage. This “expectational” (orinertial) element may enter because they do not fully pass through costchanges into price increases in the short run, as in the indexation scenar-ios in Chapter 2. A positive pass-through of labor costs into prices showsup in the Chapter 9 econometrics. The price level (and implicitly themarkup rate) appears to respond negatively to u, consistent with notstrongly cyclical price behavior.

Let χp = P/Pe and χw = w/we; these variables will equal one in a steadystate in which observations and expectations coincide for prices andwages. Easy substitution gives wb/Pe = ψχp and web/P = ψ/χw for the tar-get variables in the labor and commodity markets respectively. For amodel in the (u, ψ) plane, fairly general expressions for nominal wageand price inflation can be written as

œ = f w(u, ψχp) + (1 − σ)À (2)

and

¾ = fp(u, ψ/χw). (3)

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In (2), À = ÕL = ¼ − ü is the rate of labor productivity growth; a frac-tion 1 − σ of any productivity increase is immediately passed throughinto a higher money wage. Wages increasing in line with productivity area common union bargaining claim. The case of full pass-through (σ = 0)is sometimes but far from universally observed.

Along the lines of Kaldor’s technical progress function, we can write

À = fÀ(u, ψ/χw). (4)

The general view is that productivity varies pro-cyclically. However, thisobservation has to be interpreted in terms of the typical pattern of the ca-pacity utilization/distributive cycle described above. Along with a down-swing in capacity utilization, the wage share rises. A lagged positive re-sponse of ξL to ψ would be associated with an upswing in productivity asthe cycle bottoms out, the pattern typically observed. A positive re-sponse to u is then consistent with continued productivity growth duringthe first part of the upswing. In other words, positive values for both par-tial derivatives of fÀ in (4) are consistent with observed behavior of ξL, u,and ψ.

Equations (2)–(4) are “fairly general,” because they say that the infla-tion rates observed in the labor and commodity markets both dependcontinuously on two variables—an expectation about ψ and an observa-tion of u. A steady state in this model is defined by χp = χw = 1 and a con-stant value of ψ. To analyze stability, the first step is to substitute (2)–(4)into the definitional equation Þ = œ + Á − ¾ to derive

Ü = ψ[fw(u, ψχp) − fp(u, ψ/χw) − σfÀ(u, ψ/χw]= y[fw(u, ψχp, ψ/χw) − σfÀ(u, ψ/χw)] (5)

in which fω = fw − fp. The natural equations for changes in χw and χp area version of adaptive expectations,

÷wρw(1 − χw) (6)

and

÷p = ρp(1 − χp), (7)

where ρw and ρp are positive response coefficients.4 Equations (5)–(7) area 3 × 3 dynamic system for Ü, ÷w, and ÷p. Around a steady state, the signof ∂Ü/∂ψ is determined by f fψ

ωψσ− À , where the subscripts stand for par-

tial derivatives. The sign of this expression is ambiguous. It can be nega-tive if real wage growth has a less strong positive response than produc-tivity growth to a higher value of ψ, as appears to be in case in the longterm for the United States. Another possibility is a negative productivityresponse to ψ, or a positive response to the profit share.5 With f ψ

À < 0 one

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could have ∂Ü/∂ψ > 0 or the wage share will be locally unstable. Even inthis case, the adaptive expectations in (6) and (7) could stabilize the 3 ×3 system, and as will be seen there can be stabilizing feedbacks via effec-tive demand as well.

The analysis so far refers to the distribution/inflation “core” of theeconomy in Garegnani’s (1984) usage as discussed in Chapter 2. The im-mediate questions are about relationships between the level of economicactivity and distribution. As pointed out above, the locus along which Ü= 0 traces a curve—a “Distributive” curve in the (u, ψ) plane—not aNAIRU-style point with fixed u and ψ and a stable “nonaccelerating” in-flation rate. (How the curve can be forced to collapse to a point is takenup below.) Its slope is

dud

f f

f fu uψ

σ

σ

ψ ψ=−

w À

w À . (8)

The sign of the numerator is ambiguous, as just discussed (with locallystable dynamics of ψ calling for a negative value). For the United States,0 < fu

À < fuw , suggesting a positive denominator. With a negative nu-

merator, the resulting positive slope du/dψ is a phenomenon given differ-ent names by different authors. The new Keynesian labor economistsBlanchflower and Oswald (1994) call the distributive schedule a “wagecurve,” while for the Kaleckian radicals Boddy and Crotty (1975) itsslope encapsulates a “cyclical profit squeeze.” This usage carries overinto the applied “social structure of accumulation” macro models ofBowles, Gordon, and Weisskopf (1990) and Gordon (1995).

More generally, the slope of the distributive schedule reflects severalhistorical positions in the macroeconomic debate. Suppose for the mo-ment that the numerator of (8) is negative, or ∂Ü/∂ψ < 0. Then for lowvalues of u and ψ, a shallow positive or negative slope may occur be-cause labor’s bargaining power is weak. This situation approximates theelastic labor supply curve of the neo-Marxist growth model discussed inChapter 5.

A rising section of the curve could underlie Marxist cyclical growth,in which an increasing real wage induces capitalists to increase invest-ment levels and search for new labor-saving technologies as well as to re-duce employment via input substitution. For various reasons, includinga profit squeeze on investment at high levels of economic activity, exces-sive funds tied up in machinery, and sectoral imbalances, such a boomwill finally collapse (Sylos-Labini 1984). The productivity advances dur-ing its course, however, can support a higher production level during thenext upswing. If the economy cycles around a high activity level, will the

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full employment profit squeeze transform itself into a long-term FROPof the sort possible in the Japanese case discussed in Chapter 2?

Finally, the Distributive curve might display a consistently negativeslope, for two reasons. As already discussed, one involves positive valuesof both the numerator and the denominator in (8)—this situation mightbe labeled an “unstable profit squeeze.” The other cause for a negativeslope is a combination of a negative denominator in (9) with a positivenumerator (so that ∂Ü/∂ψ < 0). The negative sign of f ψ

w − σ ψf À signalsforced saving macroeconomic adjustment, perhaps more likely as theeconomy nears full capacity use (as discussed in Chapter 5). For high val-ues of u, price inflation would accelerate more rapidly than wage infla-tion, strengthening downward pressure on the labor share.

A steep positive or negative slope for the Distributive schedule is a spe-cial case in the present model. Yet some such configuration is essentialfor picking out a NAIRU level of capacity utilization, which would cor-respond to a vertical curve, originating at some “full employment” out-put/capital ratio Ä. In the most orthodox interpretation, marginal pro-ductivity conditions such as those in force along the “Labor demand”curve in the Figure 2.2 version of NAIRU theory would also fix the wageshare Ý. The solution set to our “fairly general” differential equationsystem (5)–(7) would reduce to a single point in the (u, ψ) plane.

The same result emerges under the new Keynesian variant in Figure2.3. Ignoring productivity growth for simplicity, let œn = ¾n = n be aNAIRU rate of inflation. Then one could rewrite equations (2) and (3) inthe form

dœ/dt = αw[f w(u, ψχp) − n] (2n)

and

d¾/dt = αp[f p(u, ψ/χw) − n]. (3n)

The functions f w and f p now stand for NAIRU-consistent configurationsof (say) an efficiency wage and a markup schedule. If the curves some-how shift away from their “equilibrium” positions, then price and wageinflation will accelerate or decelerate accordingly. In equilibrium, the in-tersection of the curves defines the (Ä, Ý) point.

Another observation about price inflation is worth adding. Along aDistributive locus with Ü = 0, ψ is implicitly a function of u at steadystate. Plugging this relationship into (3) with χw = 1 gives a reduced formfor the steady-state price inflation rate, ¾ = ¾(u). NAIRU models shrinkthis function to a point, ¾ = ¾(Ä). One ought to be able to do better thanthat.

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Figure 7.1 illustrates a not implausible relationship: for relatively lowlevels of u, d¾/du > 0 as costs increase. For intermediate levels of u,a countercyclical markup and/or pro-cyclical productivity growth canmake d¾/du negative. Finally at very high levels of capacity utilizationand/or employment, inflation speeds up as either wage inflation (theprofit squeeze) or price inflation (forced saving) takes off.

Free-form fitting of a cubic equation suggests that the diagram mightnot be a bad description of inflation in the U.S. economy.6 However, in-sofar as it reflects more than just the multicollinearity of its explanatoryvariables, the snake depicted in Figure 7.1 represents a long-run relation-ship, like the one Phillips (1958) discussed in the original paper on hisfamous curve. In the context of the model just presented, there is no rea-son to expect price or wage changes year-on-year to demonstrate anysimple pattern. The celebrated “failure” in the 1970s of short-run Phil-lips curves à la Samuelson and Solow (1960) was a case of monetaristand rational expectationalist hunters and hounds pursuing a fox that didnot exist. Where the phantom chase led has already been explored inChapter 6. After going down those trails it makes sense to work throughhow demand and distribution interact in a Keynesian/Kaleckian model.

3. Absorbing Productivity Growth

One question of interest is whether faster productivity growth raises realwage and output levels. In steady state the labor share will satisfy the re-

238 chapter seven

Output/capitalratio u

Inflation rateP

Profit squeeze orforced savings

Rising costRising productivity or

falling markup

Figure 7.1A possible relation-ship between priceinflation and the out-put/capital ratio.

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lationships Þ = œ + Á − ¾ = Û − À = 0 so that the real wage increases atthe same rate as productivity growth—a standard result already pointedout in connection with the Ramsey and Kaldor growth models. Withouttheir presumption of full employment, however, other consequences offaster productivity growth can be less beneficent. To see why, we have toset out a full macro model.

Complementing the inflation/distribution “core” (5)–(7), the price/quantity side of the economy is presented in Table 7.1, copied over fromthe “markup” specification in Table 5.1 with saving and investment in(13) and (14) tied to 1 − ψ instead of π as a representation of the profitshare. As discussed at length in previous chapters, both effective demandand (through the investment function) capital stock growth can be eitherwage- or profit-led. The detailed conditions for du/dψ and dg/dψ to havethe same sign are not identical, but quite similar. To avoid endless taxon-omies, we simply assume forthwith that the signs of both growth andoutput responses to changes in ψ are the same.

Adding effective demand makes distributional dynamics more compli-cated. In (5), one has to consider not only direct effects of the labor shareψ on its time-derivative Ü via the functions f w, f p, and f À, but also indirecteffects involving du/dψ through the equations of Table 7.1. In the locallystable distributive case with ∂Ü/∂ψ < 0 (assumed throughout this sec-tion), these linkages will not destabilize the entire system if the slope ofthe Distributive locus from (8) is “large” in absolute terms, that is, thecurve has a visually shallow negative or positive slope in the (u, ψ) plane.

Figure 7.2 illustrates the argument. In the upper diagram for a profit-led economy, an outward shift in the effective demand curve makes out-

effective demand and the distributive curve 239

Table 7.1 Basic demand side and price relationships for a one-sector model.

P = (1 + τ)wb = wb/(1 − π) = wb/ψ (9)

L/X = b (10)

u = X/K (11)

r = [τ/(1 + τ)]u = πu = (1 − ψ)u (12)

gs = [sπ(1 − ψ) + swψ]u = s(ψ)u (13)

gi = gi(u,r) = gi(u, ψ) = g0 + αr + βu = g0 + [α(1 − ψ) + β]u (14)

γg + gi − gs = 0 (15)

Definitions

π = rPK/PX = τ/(1 + τ)ω = w/P = (1 − π)/b = ψ/bψ = 1 − πγg = PG/PK

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put jump from A to B. With a negatively sloped Distributive curve due toforced saving, the labor share will begin to fall, leading to a new steadystate at C. In this case, forced saving and profit-led demand go togetherto create a strong long-term impact of expansionary policy. It is easy toimagine that if the Distributive curve were to cut the Effective demand

240 chapter seven

CA

B

AC

B

Labor shareψ

Output/capitalratio u

Effective demand

Distributive

Labor shareψ

Output/capitalratio u

Distributive

Effective demand

Figure 7.2Stable expansionaryadjustment in profit-led (upper) andwage-led (lower)economies.

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schedule from above instead of below, the labor share would diverge to-ward zero. If the Distributive curve has a positive slope, on the otherhand, medium-term stability in a profit-led economy is assured (see theupper diagram in Figure 7.4 below).

Similarly, in the wage-led lower diagram, a Distributive schedule witha shallow positive slope dψ/du will amplify the effects of expansionarypolicy over the long term. If the schedule were steep enough to intersectthe Effective demand curve from below, then an expansion would makethe labor share rise, generating more demand and output, increasing thelabor share further, and so on. Ultimately the economy would hit someform of output barrier, possibly forcing a shift over to forced saving ad-justment modes as discussed in connection with Figure 4.2.

Such a scenario can be the Achilles’ heal of expansionary, redistribu-tive policies in wage-led systems. An example is a heterodox shock anti-inflation package, where getting rid of rapid inflation by fiat boosts ag-gregate demand by eliminating forced saving and the inflation tax. Astrong push for real wage increases after the shock could set off diverg-ing wage-led output growth; well before forced saving kicks in, the stabi-lization program will probably have fallen apart.

Assuming such catastrophes away as in Figure 7.2, we can turn to thequestion of productivity growth. With a positively sloped Distributiveschedule, Figure 7.3 illustrates the implications of an upward shift in thefunction f À. By cutting costs, this jump moves a stable Distributive locusdownward. In the profit-led case in the upper diagram, the outcomesof the move from point A to a new steady state at B include a lowerwage share due to reduced labor input with faster real wage growth, ahigher level of economic activity, and faster capital stock growth—morerapid technical change is absorbed easily. In the open economy context,this could be the story of a successful exporter of manufactured goods.Lower unit labor costs stimulate the export component of aggregate de-mand, and the economy grows rapidly.

The scenario in the wage-led economy at the bottom is less pleasant.In the short run, if σ > 0 in (2), a lower labor/output ratio is not immedi-ately followed by a proportionately higher real wage. At the initial levelof output at point A, total wage payments fall as jobs are eliminated, re-ducing consumer demand. Because they stop being stimulated by de-mand pressure, investment and new capacity formation drop off.

These results persist in the new steady state at B, where along with thelabor share, the output/capital ratio and (by our “same signs” assump-tion) the capital stock growth rate are lower. The real wage will risefaster if À retains a higher value at B after both u and ψ go down, but itdoes so in the face of less employment expansion (output growth is

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down and productivity growth may be up) and slower growth of con-sumer demand.

This scenario seems to run counter to capitalism’s classic mechanismfor real per capita income to rise, that is, sustained growth of real wagesin line with productivity increases. What the bottom diagram of Figure

242 chapter seven

Labor shareψ

Output/capitalratio u

Effective demand

Distributive

Labor shareψ

Output/capitalratio u

Distributive

Effective demand

B

A

A

B

Figure 7.3Effect of more rapidlabor productivitygrowth in profit-led(upper) and wage-led(lower) economies.

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7.3 shows is that even if wages do go up to offset lower labor/output ra-tios, faster productivity growth does not necessarily lead to higher out-put and employment. This possibility dawned on the Luddites and econ-omists such as David Ricardo two centuries ago.7 If a tendency towardlagging consumer sales is not offset by other shifts such as falling savingsrates, productivity growth not “realized” by effective demand could be aproblem in wage-led developing economies today.

4. Effects of Expansionary Policy

As argued by Bowles and Boyer (1995) and substantiated for the UnitedStates in Chapter 9, demand in modern industrial economies appearsto be profit-led. Even if they so avoid Luddite problems of absorbingproductivity growth, profit-led systems are still affected by the shapeand position of the Distributive schedule. The upper diagram of Figure7.2 already illustrates a strong response to expansionary policy under aforced saving distributive adjustment. Figure 7.4 shows two additionalpossibilities when there is a profit squeeze.

In the upper diagram, a “permanent” outward shift in the Effectivedemand schedule because of expansionary policy will not have strong ef-fects on employment and can even reduce medium-term growth. In theshort run, economic stimulus looks good, as output jumps from point Ato point B and investment rises (assuming that higher capacity utilizationhas some positive impact on investment demand). Over a longer stretchof time, however, unit labor costs ψ increase toward point C. Private in-vestment could well decline in reaction to the high employment profitsqueeze. The dynamic adjustment through points A, B, and toward Cmay lead toward slower growth in the medium run.

In the lower diagram, adjustment around the Ü = 0 locus is not sta-ble. As discussed in connection with equation (8), this “unstable profitsqueeze” is associated with a negatively sloped Distributive schedule.The overall system can be stable, however, if the Distributive curve cutsthe (profit-led) Effective demand curve from above. At least in termsof stimulating output and growth, expansionary policy is now clearlycounterproductive since it drives the economy to a new equilibrium C ly-ing to the left of the initial point A. The wage share does increase, butoutput and productivity growth could be substantially reduced.

There are potential feedback effects that could worsen these problems.First, a positively sloped Distributive schedule may shift further up-

ward or become steeper, as higher observed wages lead to labor mili-tancy and still higher wage targets in contract negotiations. The impor-tance of such processes depends on the social context. They were far less

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forceful in the United States of the 1990s than they were when theGolden Age of postwar economic growth (Glyn et al. 1990) ended morethan a quarter-century ago. As discussed in Chapter 9, the economy mayhave shifted from a borderline unstable to a stable profit squeeze con-figuration at the end of the Golden Age.

Second, the Effective demand schedule and capital formation may

244 chapter seven

Labor shareψ

Output/capitalratio u

Effective demand

Distributive

Labor shareψ

Output/capitalratio u

Distributive

Effective demand

C

B

A

C

B

BA

Figure 7.4Expansionary policyin a profit-led econ-omy when distribu-tive dynamics arestable (upper) andunstable (lower).

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shift downward. Reduced investment demand in the short run maydampen “animal spirits” at home and lead to diversion of capital spend-ing to projects abroad over the medium term. This observation is per-tinent to industrialized economies today because of the opening of in-ternational capital markets over the 1970s and 1980s. Profitabilitycomparisons between potential domestic and foreign projects play amuch bigger role in enterprise decision making than they did even in the1980s.

Third, such responses may be exacerbated if higher real wages and/orcapacity utilization are associated with faster inflation toward the farright end of the curve in Figure 7.1. Combined with exogenous upwardshifts in the cost schedule induced by the oil price shocks, such struc-turalist price and wage pressures triggered the staggering “anti-infla-tionary” American interest rate hikes just before and after 1980. Tightmoney was anti-employment, and curtailed investment spending. To ex-plore such eventualities further, we have to bring in the financial side ofthe economy, as in following sections of this chapter. However, it shouldalso be added that the experience of the late 1990s belied any strong ten-dency for inflation to speed up at relatively high levels of aggregate de-mand.

Fourth, widening trade deficits can be caused by higher wages andemployment, meaning that interest rates may have to be increased tostaunch the external gap. In the United States, such a scenario has be-come increasingly relevant as the economy has opened to foreign trade(the marginal import coefficient with respect to GDP in the 1990s is onthe order of one-third). Alternatively, devaluation provokes further infla-tion. Because international capital movements have become highly re-sponsive to interest rate differentials and expected exchange rate adjust-ments, there may be a contractionary bias to the world financial system(Eatwell and Taylor 2000).

Finally, on the brighter side, there are policies that can be used to off-set many of these unfavorable effects. With regard to effective demand,intelligently directed public investment (in both physical and “human”capital) can help sustain overall accumulation, especially if it “crowdsin” private capital via complementarities. Insofar as the fiscal deficit andassociated interest obligations on outstanding debt (see Chapter 6) areconsidered “excessive,” such spending initiatives in the United Statescould be financed by taxes on financial transactions (the volume ofwhich has skyrocketed over the recent period) and/or wealth (Pollin1998b; Wolff 1995).

On the “supply” or distribution/inflation side of the economy, steps toencourage greater worker “voice” in enterprise management can leadto less labor militancy and even higher investable profits by flattening

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or shifting the Distributive schedule downward (Freeman and Medoff1984). Asset redistribution may enhance economic productivity over-all (Bowles and Gintis 1995). Controls and/or taxes on external cap-ital movements can make internal investment less sensitive to changesin interest and profit rates. Some of these proposals transcend meremacroeconomics, but illustrate how intimately it depends on the socialfabric.

5. Financial Extensions

The next task is to bring in the dynamics of fiscal and monetary interven-tions as they cumulate through the private sector’s, government’s, andthe banking system’s flows of funds. Alongside the income level andshare changes illustrated in Figures 7.2 and 7.4, the real interest rate i −¾ enters as an indicator of distributive strife. As in Chapters 4 and 5, theIS/LM analysis to follow is fairly conventional. The emphasis in thepresentation is on how a generalized model of the real and financialeconomy hangs together. With more specific assumptions, detailed re-sults from post-Keynesian and Minskyan specifications are presented inChapters 8 and 9.

The LM curve introduced as equation (11) in Chapter Five can be re-stated as

µ(i − ¾, u)[(qPK/T) + 1] − ζ(Tc/T) = 0, (16)

where i is “the” nominal interest rate, qP is the asset price of capital, T isthe outstanding stock of fiscal debt (“T-bills”), Tc is the part of T held bythe central bank, and ζ is the credit multiplier blowing up high-poweredmoney Tc to the outstanding money stock.

The balance sheets underlying (16) appear in Table 7.2. The main con-trast with Table 4.2 is that households now lend Lh to business, insteadof holding equity PvV. The nominal interest rate on bank and household

246 chapter seven

Table 7.2 Balance sheets for an IS/LM model.

Households BusinessM Ω qPK Lb

Th Lh

Lh

Commercial Banks Central Bank GovernmentH M Tc H TLb

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loans and T-bills is assumed to be the same, with q as the accommodat-ing variable.

The other new wrinkle in (16) is inclusion of the real interest rate as anargument in the money demand function µ. If households don’t suffermoney illusion, the real rate should also figure in the definition of q as

q = r/(i − ¾). (17)

This formula looks suspiciously close to Irving Fisher’s arbitrage equal-ity r = i − ¾ between the profit rate and the real interest rate (derived inChapter 3).8

In the financial world of Table 7.2, Fisher’s formula would apply inasset market “equilibrium” when q = 1. In the more general setup of Ta-ble 4.2, however, the equation for q is longer,

q = r/[λ(i − ¾) + (1 − λ)iv], (18)

where λ is the share of loans in qPK and iv is the return to equity. From(18), one gets the Fisher relationship only when q = 1 and i − ¾= iv. Theequity premium puzzle discussed in Chapter 4 makes sure that the lattercondition does not apply. Moreover, the r = 1 − ¾ equation does not fitthe data from the U.S. economy. Faster inflation does not boost nominalinterest rates automatically, a point relevant to the discussion to follow.

In any case, plugging (17) into (16) while observing that r = (1 − ψ)uas an accounting identity produces a final form for an LM equation,

µ(i − ¾, u, ¾)[(1 − ψ)uZ/(i − ¾)] + 1 − ζ(Tc/T) = 0, (19)

where Z = PK/T. In this formula, money demand increases as a functionof ¾ through the terms in i − ¾. This is a nonstandard result, although itis consistent with Keynes’s emphasis on the likelihood of asset holders’“fleeing to liquidity” when anything untoward happens. A less restrictedfinancial model than the one in Table 7.2 would include “hedge assets”such as equity, land, collectibles, and so on, which could be used as infla-tion shields.

A full short-run macro model emerges if we adjoin (19) to the equa-tions of Table 7.1. A couple of revisions, however, are useful. First,bringing in effects of inflation, the investment function (14) can be modi-fied to the form

gi = g0 + [α(1 − ψ) + β]u − θ(i − ¾) − φ¾, (14′)

where the net impact of a higher value of ¾ on investment will be nega-tive when φ > θ > 0. Throwing an extra ¾ argument into the money de-

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mand function µ (with a negative partial derivative) similarly offsets theodd effects of inflation mentioned above.

A second change is to carry interest payments in the accounting, atleast for T-bills, so that as in Chapter 6 we can study the macroeconomicrole of government debt. If only rentiers hold T-bills, then the savingfunction (13) should be revised to read

gs = [sπ(1 − ψ) + swψ]u + sπ(i/Z), (13′)

where it is tacitly assumed that all T-bill interest ultimately gets passedalong to wealthy households and that we can continue to ignore interestpayments on loans to business.9

6. Dynamics of the System

To get to full dynamic speed, we have to investigate how the ratio orstate variable Z = PK/T evolves over time. After substitution among theentries in Table 7.2, total household wealth can be written as Ω = qPK+ T, or the sum of the economy’s “primary assets” comprising physicalcapital and “outside” debt. The ratio Z basically measures Ω’s compo-sition.

As discussed in Chapter 10, in an open economy national wealth isgiven by Ω = qPK + T + N, with N standing for net foreign assets. Ta-bles 1.5 and 1.6 show that (in trillions of dollars) the U.S. numbers at theend of 1999 were qPK = 26.6, T = 4.9, N =−1.3, and Ω= 30.2 so that(qPK − N)/T ≈ 5.1. In practical terms, a value of Z in the range of ten orabove would suggest a very thin national bond market; a value belowthree might be taken as an indicator that government debt is “too high,”as it allegedly is in Japan.

Along lines already developed in section 5 of Chapter 6, a differentialequation for Z can be written as

‰ = Z[g − (i − ¾) − γgZ], (20)

with γgPK as the primary fiscal deficit. To explore stability, we have toconsider the effects of Z and ψ on i, ¾, and g. In the LM equation (19), ahigher value of Z increases money demand by raising the (1 − ψ)uZ/(i −¾) term, leading to a higher interest rate. Investment demand gi will fall,reducing u as well. The impact effect of a lower u on markup inflation ¾can take either sign in (2), but is likely to be weak. Absent strong interestrate cost-push as discussed in section 3 of Chapter 3, we have d¾/dZsmall and of uncertain sign, dg/dZ < 0, di/dZ > 0, and dË/dz > 0 for γg

> 0. Plugging all this information into (20) gives d‰/dZ < 0. This self-

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stabilizing response could vanish if interest rate cost-push were strong,an idea lurking at the fringes of macroeconomics since the times ofThomas Tooke.

The stability of (20) has interesting implications. The ratio variable Z= PK/T can be interpreted as the “velocity” of fiscal debt with respect tothe capital stock, in the sense that if it takes a high value then there isweak financial backup for tangible assets (just as a high ratio of GDP tothe money supply signals that money is “scarce”). As long as the out-put/capital ratio u and the policy variables ζ and Tc/T do not vary overwide ranges, then if Z does not change very much, neither will other ve-locity ratios such as PX/H, PX/M, and so on. From the perspective of ademand-driven growth model, the widely heralded stability of moneyvelocity, to the extent that it exists, is simply a consequence of the factthat the differential equation determining the evolution of its underlyingdeterminant Z is stable and relatively unaffected by changes in incomedistribution and output.

Turning to the effects of changes in ψ on Z, dg/dψ can take either sign,depending on whether the economy is wage- or profit-led. By increasingunit labor costs, a higher ψ makes ¾ increase in (2). In (19), it reducesmoney demand and thereby i. These interest rate and inflation effectsmay be weak, so that if investment demand is strongly profit-led the netoutcome can be a negative value of d‰/dψ in (20). In the interest of brev-ity, we consider only the locally stable case in which dÜ/dψ< 0 in (5). Anincrease in Z affects Ü by driving up the interest rate and reducing u.With a stronger output effect on wage than markup inflation, we getdÜ/dZ < 0.

The sign pattern of the Jacobian matrix of (5) and (20) around asteady state becomes

ψ ZÜ − −

− −&Z (?)

where the potential destabilizing effect of interest rate cost-push is ig-nored. The question mark in the row for ‰ refers to possible effects of alower real interest rate combined with weakly profit-led investment ond‰/dψ.

7. Comparative Dynamics

A whole macro model is bundled into equations (5) and (20); work-ing through the implications of all the own- and cross-effects is not

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easy. At most, the exercises to follow may help clarify whether expan-sionary and/or progressively redistributive policies have a chance to suc-ceed in an economy in which effective demand is profit-led and the wageshare and capacity utilization have a positive relationship along the dis-tributive curve. The outcomes are not completely unfavorable, but maywell have politically hard-to-handle adverse effects on the real return tofinancial assets.10

We first have to trace effects through the IS/LM system. In a standarddiagram like Figure 4.7 for a profit-led economy, the IS curve will shiftrightward (increasing both u and i) when the labor share ψ and inflationrate ¾ decrease and/or government outlays γg go up. The LM curve willshift downward (reducing i and increasing u) when the capital/T-bill ra-tio Z declines, ¾ decreases, ψ increases (reducing q), and the credit multi-plier ζ or the part of T-bills used as high-powered money Tc/T goes up.

Taking into account shifts in both curves, the overall effects are likelyto go as follows:

ψ Z ¾ γg ζ Tc/Tu − − − + + +i ? + ? + − −g − − − + + +

It is assumed that the outward shift in the IS curve makes du/dψ< 0, andthe ambiguous effects of both curves shifting make it hard to determinehow i responds to ψ and ¾. Effects of changes in the policy and state vari-ables on the growth rate g are assumed to parallel those on u. From (3)we further have a positive effect of ψ and an ambiguous effect of u on theprice inflation rate; these feedbacks are assumed not to override the signsjust indicated.

Figure 7.5 shows how the schedules for Ü = 0 (“Distributive”) and ‰= 0 (“Velocity” of the fiscal debt) adjust in response to policy changes.From the signs and likely magnitudes of the derivatives discussed at theend of section 6, the Velocity schedule is not strongly affected by changesin the labor share in the (Z, ψ) plane. Its slope is negative and steep (orpositive and steep) insofar as d‰/dψ is small and negative (or small andpositive if investment demand is only weakly profit-led). Because bothdÜ/dΖ and dÜ/dψ are negative, the Distributive schedule slopes down-ward. With ψ and u varying together, the output increase associated withlower interest rates from a lower value of Z may make the Distributiveschedule nonlinear.

A “permanent” increase in public spending γg pushes the Velocityschedule to the left by making public debt build up faster (reducing Z),

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and moves the Distribution schedule up by raising aggregate demand.Both shifts raise the labor share in the transition from point A to point B,partly offsetting the output and growth stimulus from the higher value ofγg (as in Figure 7.4). The capital/debt ratio unambiguously decreases.Along with a higher ψ, the lower value of Z will bid down the nominalinterest rate as long as Tc/T or the share of the fiscal debt that is “mone-tized” is not reduced. Inflation, on the other hand, could well speed upbecause of cost pressures. The real interest rate i − ¾ could decline, dis-pleasing bondholders. This last change could be the main political obsta-cle to a policy shift which otherwise has generally favorable effects (inso-far as they are not partly or wholly reversed by the rising labor share, asin Figure 7.4).

Does expansionary monetary policy fare any better than its fiscalcounterpart? By shifting the LM curve downward, the impact effects of ahigher ζ or Tc/T include a lower interest rate, higher rates of economicactivity and capital stock growth, and an ambiguous change in the rateof inflation. In equation (20) the balance of forces is unclear, but rela-tively strong growth and inflation effects might require a shift of Z to theright to hold ‰ = 0, as shown in Figure 7.6. As in Figure 7.5, the expan-sionary policy makes the Distributive schedule shift up.

The new equilibrium at point B has a higher level of Z (if the shift inthe Velocity schedule dominates) and a higher ψ (with the increase atten-uated by the negative slope of the Distributive curve). Increased fiscal

effective demand and the distributive curve 251

Labor shareψ

Capital/debtratio Z

Velocity

Distributive

B

A

Figure 7.5Effects of a highervalue of publicspending γg acrosssteady states.

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debt velocity bids up the interest rate, partly offsetting the initial mone-tary expansion. If the real interest rate is stable or rises (due to the in-crease in Z and weak effects of expansion on inflation), monetary expan-sion may prove politically feasible. A high interest rate is more likely ifthe Velocity schedule has a positive slope due to a weak effect of thehigher labor share on investment demand.

Finally, Figure 7.7 shows what happens if labor costs fall, because offaster productivity growth, wage restraint, or institutional changes suchas those discussed at the end of section 4. The Distributive scheduleshifts downward, stimulating growth and reducing inflation as in the up-per diagram of Figure 7.3. The higher capital/debt ratio bids up the inter-est rate. Bondholders might be happy, especially because people in theirclass position would also gain from a higher profit share in current in-come. Combined with neutral monetary and mildly restrictive fiscal poli-cies, this scenario is not far from the U.S. experience in the late 1990s.

As mentioned above, the impacts of the policy changes illustrated inFigures 7.5–7.7 are a mixed bag. In a profit-led economy in which strongfinancial interests push for relatively high real interest rates and low in-flation, expansionary policies may well have to be combined with insti-tutional changes to hold down production costs. One way to shift downthe Distributive schedule is through money-wage cuts along the lineshinted at by Modigliani (1944) in the quotation presented in Chapter4.11 The Modigliani (or Patinkin) line is that the nominal wage is “toohigh” with respect to the money supply; in terms of Figure 7.7, ψ should

252 chapter seven

Labor shareψ

Capital/debtratio Z

Velocity

Distributive

B

A

Figure 7.6Possible effects ofexpansionary mone-tary policy acrosssteady states.

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decline for a given level of Z. Alternatively, NAIRU-style arguments as-sert that the real wage can be “too high” to clear the labor market; aswe have seen in Chapter 6, a temporary price inflation may then be“needed” to erode it away.

The reasoning at the end of section 4 suggests that there are institu-tionally less painful ways than cutting money wages or running price in-flations to shift the Distributive schedule downward to sustain invest-ment demand. If powerful social actors favoring a low labor share and ahigh real interest rate can be kept in check, then both distributionallyprogressive and expansionary policies have a role to play, especially ifthey can be designed to stimulate productivity growth and accumula-tion.

8. Open Economy Complications

Financial considerations carry over full force to the open macro-economy, as described in Chapter 10. Here, we deal only with the de-mand side in the short run, to give a foretaste of things to come and toround out consideration of potential linkages between income distribu-tion and the level of economic activity.12

The economy is assumed to export its product in volume E, with À =E/K (note the redefinition of À) depending positively on the real exchangerate ρ = e/P where e is the nominal dollar/yen exchange rate.13 The elas-ticity of À with respect to ρ is η. If excess capacity is low, exports may de-

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Labor shareψ

Capital/debtratio Z

Velocity

Distributive

B

A

Figure 7.7Steady-state effectsof a reduction in la-bor costs.

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cline when domestic activity picks up as producers more aggressivelypursue internal sales, but this extension of the basic model is omitted forsimplicity.

On the import side, as usual we assume a “workshop” economywhich processes intermediate and raw material imports into final prod-ucts for domestic use or export, or else a developing country that haspursued import-substituting industrialization far enough to be depen-dent on imported intermediate inputs. Import volume is the quantity aX,where a is an input-output coefficient which again for simplicity is as-sumed to be fixed. Total cost of output decomposes as PX = wbX +πPX + eaX, so we implicitly assume that the value of output PX is big-ger than GDP because it includes the cost eaX of imports.

Table 7.3 sets out equations for the model. We return to using theprofit share π as the key internal distributive variable, because in (21) theprice level is determined as a markup on the sum of labor (wb) and im-port (ea) costs per unit of output. The definitions in (22) and (23) showthat with a constant π, the real wage ω is an inverse function of the realexchange rate ρ. There is now a three-way distributional conflict amongprofit recipients, wage earners, and the rest of the world.

Scaled to the capital stock K, total real injections minus leakages ∆are equal to À + gi − gs; for macro equilibrium, (29) shows that ∆ mustequal zero. Total differentiation gives d∆= 0 = (d∆/du)du + (d∆/dρ)dρ,or du/dρ = −(d∆/dρ)/(d∆/du). Standard Keynes/Harrod stability argu-ments require that d∆/du < 0, so that the sign of du/dρ is the same asthat of

d∆/dρ = (À/ρ)η − [ρau(1 − sw)/À]. (30)

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Table 7.3 Macro relationships for a one-sector, open economy model.

P = (wb + ea)/(1 − π) (21)

φ = ea/(ea + wb) (22)

ρ = e/P = φ(1 − π)/a; ω = w/P = (1 − φ)(1 − π)/b (23)

u = X/K (24)

r = πu (25)

gs = sππ + [sw(1 − φ) + φ](1 − π)u (26)

gi = gi(r, u) = gi (π, u) (27)

À = E/K = À(ρ) (28)

À + gi − gs = 0 (29)

Definition

π = rPK/PX = τ/(1 + τ), where P = (1 + τ)(wb + ea)

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Effects of the change in ρ on investment demand are left out in this ex-pression to keep the algebra within bounds (shifts in gi are implicit in thediagrammatic analysis coming later).

Equation (30) shows how ∆ and thereby u respond to currency deval-uation in the form of an increase in the real exchange rate ρ. If a countrydevalues from an initial trade deficit (so that eaX > PE in current prices)and its workers’ saving rate sw is small, then the term ρau(1 − sw)/À =(1 − sw)eaX/PE could easily exceed one. Certainly in the short run, theexport elasticity η need not have so high a value. In other words, devalu-ation could be contractionary, improving the trade deficit not so muchby increasing exports and encouraging substitution of domestic productsfor imports as by making the level of economic activity go down.

To shed further light on this possibility of “contractionary devalua-tion,” we can consider the country’s trade deficit in real terms (againscaled by the capital stock), D = ρau − À. One can easily show that

dD/dρ = (À/ρ)[(ρau/À) − η] + ρa(du/dρ). (31)

In the literature on open economy macroeconomics, “Marshall-Lerner”(or ML) conditions in various forms are often invoked to ensure thatdD/dρ < 0 so that devaluation reduces the trade deficit. Invariably, suchconditions resemble the first term to the left of the equals sign in (31) anddo not include a term in du/dρ. Two points are worth making.

The first is that if we ignore du/dρ in (31), then a negative value ofdD/dρ requires that (ρau/À) − η< 0. This inequality is the standard issueML condition for the present model. Leaving aside the term in sw in (30),one can see that when the inequality holds, devaluation cannot be con-tractionary. A “perverse” macroeconomic result seems to be avoided be-cause the trade deficit is empirically observed to decrease (usually) in re-sponse to devaluation.

The interesting thing about this argument is its unconscious accep-tance of Say’s Law. If the level of economic activity u is assumed to beconstant, then it makes no sense to ask how its changes might influencethe trade balance. Of course if u can change, then the bracketed term in(31) can be positive, combining contractionary devaluation and dD/dρ< 0 just because du/dρ ≠ 0. In practice, this sort of scenario happensfairly often in developing economies where export elasticities can be low.

The other point is that from (31) the trade deficit may respond weaklyto devaluation when du/dρ > 0, or a devalued exchange rate stimulateseffective demand. For a given profit share π, a “weaker” (or higher) ρgoes hand in hand with a lower real wage ω, so one might expect du/dρ> 0 in a profit-led system. To see how this works out in detail, we can

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Trade deficitQ or D

Output/capitalratio u

Trade deficitQ or D

Output/capitalratio u

B

A

D

Q

BA

D

Q

Figure 7.8Effects of devaluationwhen demand isprofit-led (upper) andwage-led (lower).

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use the definitions in (22) and (23) to rewrite the macro balance condi-tion (29) in the form

gi − [sππ + swωb]u = Q = D = ρau − À, (32)

where Q stands for the domestic component of effective demand (invest-ment minus saving) and D is again the trade deficit.

We know that dQ/du < 0 from a Keynesian stability condition, whilefor a constant profit share, dQ/dρ will be positive (negative) when de-mand is profit-led (wage-led) because of the negative effect of ρ on ω. If aSay’s Law ML condition applies we have dD/dρ < 0, but the oppositesign is also a possibility. Finally, dD/du > 0 because imports go up (andexports may go down) in response to higher economic activity.

Figure 7.8 shows the effects of devaluation in the two cases, with mac-roeconomic equilibrium observed at the points where the Q- and D-schedules cross. In a wage-led economy at the bottom, devaluation canbe contractionary when the leftward shift in the Q-schedule is big (alower real wage strongly reduces domestic demand) and the downwardshift in the D-schedule is small (a relatively low export elasticity η). Bothshifts lead the trade deficit to improve, in the sort of “overkill” of whichthe IMF is occasionally accused (Taylor 1991). Even if the Say’s LawMarshall-Lerner condition is violated and the D-schedule shifts up, thetrade deficit can still decline because of lower effective demand.

By contrast, in the profit-led economy at the top, the rightward shiftin the Q-schedule counters the downward shift in the D-schedule, andthe trade balance improvement may be slight. Following Blecker (1991)one might argue that the Reagan tax cuts of the 1980s pushed the U.S.economy in the direction of being more profit-led by reducing tax-induced income leakages from high, profit-based incomes and reducingdifferentials in “leakage” rates across different sources of income.14 Oneconsequence in line with the upper diagram was the small reduction inthe trade deficit observed after the dollar depreciated in the mid-1980s.This result was only made worse by deteriorating American “competi-tiveness” or an upward drift in the D-schedule for a given level of u.

Once again, structural changes and distributional shifts interact incomplicated fashion to generate observed macroeconomic events.15

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chapter eight

z

Structuralist Financeand Money

The trouble with most macroeconomic models of finance is that theydon’t let anything interesting happen. In the standard LM apparatus(and even more so in new classical models), the only action involves ratesof return adjusting to clear securities markets—there are no financial in-novations such as money market funds and derivatives, no strong feed-backs between the real and financial sectors, no speculative booms andcrashes. A few economists, mostly post-Keynesians, have built endoge-nous or passive money into their model frameworks; fewer still havedealt with endogenous changes in finance. Modest steps in these direc-tions are taken in this chapter, on the basis of historical experience andstylized facts. We begin by reviewing the latter, in a logical reconstruc-tion of financial (mainly banking) history, if not quite the history itself.1

A short-run model of “endogenous money” in a complete macro ac-counting framework is then set out. It is followed by a post-Keynesiangrowth model focused on business borrowing under strong but not unre-alistic simplifying assumptions about the financial accounts. The discus-sion closes with a quick review of new Keynesian models aimed at cap-turing the institutional (or, better, social) aspects of finance. Both post-and new Keynesian formulations foreshadow a model in Chapter 9 ofMinsky’s cyclical macro story as based on some of the micro detail pre-sented here.

1. Banking History and Institutions

Over a long historical span, Chick (1986) traces the linkages amongchanges in bank liabilities (∆M =∆C +∆D, where C stands for “notes”or currency, and D for deposits), reserves (∆H), and loans (∆L) in “An-glo-American” commercial banks.2 In the eighteenth century, financehouses across the United Kingdom gradually shifted from being “gold-smith-bankers” to “country banks,” mostly sponsored by local mer-

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chants. These banks issued notes which circulated alongside merchants’bills of exchange as the main means for commercial payments (workers,insofar as they engaged in monetized transactions at all, continued to usethe coin of the realm). The notes were short-term and, like deposits ingold, were used to support short-term lending as well as a precautionarylevel of reserves:

∆M ⇒ ∆L and ∆H. (1)

In both countries, battles ensued over the right to issue notes. TheBank of England (still a private entity) spent much of the eighteenth cen-tury trying to revise the Bank Act to get a monopoly on issue. Depositbanking and a clearing system in London arose as responses to the pro-gressive strengthening of the Bank of England’s monopoly position. Inthe United States, a National Bank Act limited the right of issue to Na-tional Banks holding government debt—after all, the Union had to fi-nance the Civil War. Systems of “correspondent banking” emerged inwhich U.S. money center banks (mostly in New York and Chicago) andthe Bank of England held surplus funds of the country banks. Their“reserves” thereby shifted from being mainly specie to deposits in themoney centers or notes of the Bank of England.

The presence of fractional reserves (legislated in the United States andsubject to prudential good practice in the United Kingdom) permittedoverall credit expansion. In the United States, the Federal Reserve Sys-tem was originally set up with a dozen virtually independent regionalFeds in charge of rediscounting operations with local banks on bills orig-inating in each one’s domain. Federal bonds issued to finance World WarI soon pushed the system as a whole toward open market operations—an institutional change unanticipated by the original architects. A new,truly “central” bank run by the Board of Governors emerged in Wash-ington, D.C., in the 1930s.

The implications of all these developments for the regulation of themoney supply began to be recognized at the same time. The left Keynes-ian Lauchlin Currie (1934) and others deciphered the standard textbookcausal chain

∆H ⇒ ∆L ⇒ ∆M = ζ∆H, (2)

where ζ is a deposit multiplier of the sort introduced in previous chap-ters. “Monetary policy” became possible insofar as the monetary au-thorities (the central bank) could influence the value of ζ or ∆H. In thissystem, a sharp exogenous reduction in reserves, say from a run against

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the local currency, forces loans and deposits to contract. As discussed inChapter 3, central bankers eventually invented “lender of last resort,” orLLR, interventions (necessity is the mother of . . .) to create compensat-ing reserves and stave off systemic collapse.

These changes, however, took time. Around the turn of the nineteenthcentury, well before Currie arrived at his insights into the control of themoney supply, the Banking School got the upper hand in the long debatewith its Currency School antagonists. If banks prudently lend short term(that is, they accept only “real bills”), then it is not so much their re-serves as the collateral on their loans that guarantees the security of theirdeposits. From this stance, it is a short step to consider a pure creditbanking system like the one built into the Wicksellian inflation model inChapter 3. If ∆Ld is the increase in loan demand, we have

∆Ld = ∆L ⇒ ∆M ⇒ ∆H, (3)

or “loans create money.” In conformity with the local rules of the game,the “required” increase in reserves is determined by institutional ar-rangements within the banking system. Loan demand itself could be reg-ulated by changes in the interest rate, again partially subject to controlby the authorities.

As detailed for the United States in the following section, a more accu-rate story for the most recent turn of the century involves “liability man-agement,” whereby banks choose a level of new loan supply ∆Ls andthen find reserves to cover:

∆Ls = ∆L ⇒ ∆M ⇒ ∆H. (4)

In the words of a former senior vice president of the New York FederalReserve, “in the real world banks extend credit, creating deposits in theprocess, and look for reserves later” (Holmes 1969). The monetary au-thorities can abet this search by creating unborrowed reserves throughopen market operations. Alternatively, they can impose a “frown cost”on commercial banks while letting them obtain borrowed reserves atthe discount window. Liability management (or the “doctrine of shift-ability” in older literature) refers to any means by which commercialbanks shift their reserve constraints onto the nonbank public. To buildup ∆H, they may search more aggressively for loans from discounts orfrom the federal funds, Eurocurrency, and certificate of deposit (CD)markets.

Financial innovations underlay all the changes summarized in (1)through (4). One essential difference between the real and the financialsides of the economy is that “new technologies” in the latter are easily

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copied—there are no long-lasting Schumpeterian returns to financial en-trepreneurship. This is one key reason why a changing structure of finan-cial claims (as just outlined) is endogenous to capitalism. This doctrinefound its prophet in Hyman Minsky (1975, 1986). Our next task is todelve more deeply into what Minsky and his followers have to say aboutthe modern causal structures (3) and (4). In Pollin’s (1991) usage, wewill also have to investigate the differences between Minsky’s “structur-alist” approach to monetary/financial innovation and Kaldor’s (1982)and Moore’s (1988) “accommodationist” (or more strictly BankingSchool) narrative in which the central bank usually acts to ratify the on-going pace of credit creation at some fixed interest rate.3

It is also fair to add that in practice as opposed to in theory, the work-ing monetary model of the macro economy espoused by central banks isfor practical purposes post-Keynesian, at least according to Fair’s (2000,pp. 2–3) description. The current standard model is based on three basicequations, which are: (1) an “interest rate rule: The Fed adjusts the realinterest rate in response to inflation and the output gap (deviation of out-put from potential). The real interest rate depends positively on inflationand the output gap. Put another way, the nominal interest rate dependspositively on inflation and the output gap, where the coefficient on infla-tion is greater than one” (harking back to Wicksell’s endogenous moneymodel as described in Chapter 3); (2) a “price equation: Inflation de-pends on the output gap, cost shocks, and expected future inflation”;and (3) an “aggregate demand equation: aggregate demand (real) de-pends on the real interest rate, expected future demand, and exogenousshocks. The real interest rate effect is negative. In empirical work thelagged interest rate is often included as an explanatory variable in the in-terest rate rule. This picks up possible interest rate smoothing behaviorof the Fed.”

2. Endogenous Finance

Two questions naturally arise: What have been the implications of twen-tieth-century financial innovations for the inflation and interest rate per-formance of the economy? How does endogenous finance enter the busi-ness cycle?

If we broadly follow Minsky (1986), Dymski and Pollin (1992), anda more analytical treatment by Schroeder (2002), the key idea is thateconomic actors are constrained by their inherited financial positions,which Minsky describes as “hedge,” “speculative,” or “Ponzi.” A unit ispracticing hedge finance when a “reasonable” lower bound on its antici-pated cash flows from operations exceeds anticipated commitments at

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all future times (“anticipated” is used in a Keynesian sense—expectedvalues over well-defined probability distributions on all future events arealien to Minsky’s world).

Speculative units anticipate that cash commitments will exceed cashflows at some points in the future, for example, when principal repay-ments on short-term debt fall due. They can run into trouble if themoney market does not function normally at critical times, such as whendebt has to be refinanced. If speculative positions are common, then up-ward pressure on interest rates can drive the whole system toward “fi-nancial fragility.”

Fragility is much more likely if many firms are engaging in Ponzifinance, with anticipated cash inflows falling short of obligations at mostor all future times. Like their namesake, Ponzi units have to borrow topay interest as well as principal on their debts. Were they wise, theywould carry big stocks of liquid assets, but they often do not. An enter-prise with highly seasonal sales, for example, may hope that some year’sbonanza will carry it through the next few. The Enron Corporation, tonote the most notorious example of 2001, apparently “marked to mar-ket” anticipated energy-trading revenues far in the future, thereby pro-viding nonexistent collateral for its Ponzi mountain of debt.

With these descriptions at the back of the mind, we can assess the evo-lution of the American financial system, beginning before the Great De-pression. As already observed in Chapter 3, business cycles at that timeinvolved significant price decreases (and, implicitly, rising real interestrates) in the downswing.4 During a recession, debtors found their obli-gations mounting in real terms and were pushed toward speculativeand Ponzi positions. Waves of debt repudiation followed. An increasingproportion of capital assets was controlled by individuals, directly orthrough corporate equity. Along with a collapse in effective demandon the part of the debtors, the entire financial system could be drasti-cally simplified, requiring years to rebuild. Irving Fisher’s (1933) “debt-deflation” chronicle is the classic description of such a process.

In the United States, debt-deflation became less important after the1930s, as the Federal Reserve and Treasury began to engage in counter-cyclical policy aimed at moderating real/financial cycles of the sort dis-cussed in Chapter 9. At the same time, “automatic stabilizers” such asunemployment insurance were created as part of the welfare state. In-teracting with the responses of the financial system itself, these bits ofeconomic engineering had unexpected consequences. One was that aninflationary bias was added to the system by the presence of demandsupports. In terms of Figure 7.2, the level of economic activity waspushed toward the right, leading to increased inflation in either the up-

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per (due to forced saving, Minsky’s interpretation) or lower (profitsqueeze) diagram.

A second unanticipated outcome was a move of corporations to-ward speculative and Ponzi positions, leading them to seek higher short-term profitability to try to keep their financial houses “in order.” Absentfears of price and sales downswings, high risk/high return projects be-came more attractive. Such a shift was notable in the increased “short-termism” of investment activities and the push toward merger and ac-quisition (M&A) activity in the 1970s and 1980s when corporate q wasless than one.

Third, the intermediaries financing such initiatives gained more ex-plicit protection against risky actions by their borrowers through LLRinterventions on the part of the Fed and (especially) savings and loan reg-ulators. The resulting “moral hazard” induced both banks and firms toseek more risky placements of resources.5 Financial institutions, in par-ticular, pursued innovation.

Just after World War II, they started out with a big load of governmentbonds in their portfolios and strict upper bounds on interest paymentson deposits (via the Fed’s “regulation Q”). By the 1970s, however, liabil-ity management rapidly emerged, for at least two important reasons.One stemmed from the credit crunch of 1965–66. In the years immedi-ately before, money center banks had started offering negotiable cer-tificates of deposit to their corporate clients. They thus preserved theirdeposit base, but only as long as the regulation Q limit on CD interestrates was above the ninety-day T-bill rate. When the gap vanished, thecommercial banks rapidly lost funding and had to start calling loans tothe securities industry—some observers see the episode as a close en-counter with a 1929-level crash.

The second reason is that at roughly the same time, unregulated Euro-dollar and then Eurocurrency markets started to thrive. A Eurodollardeposit is just a deposit denominated in dollars in a bank outside thepolitical jurisdiction of the United States. British and American authori-ties winked and nodded at such placements at the outset, because theyseemed like a sensible way for commercial banks to make use of their ex-cess reserves. A major contributing factor to growth in Eurocurrencymarkets was the American “interest equalization tax” of 1964–1973,enacted in an attempt to defend the capital controls in force at the time.Basically, the tax raised costs for banks to lend offshore from their do-mestic branches. The resulting higher external rates led dollar depositorssuch as foreign corporations to switch their funds from onshore U.S. in-stitutions to Eurobanks.

Eurocurrency transactions rapidly taught market players that they

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could shift their deposits, loans, and investments from one currency toanother in response to actual or anticipated changes in interest and ex-change rates. These moves were early warnings of a pervasive regulatoryproblem that dominates the world economy today: any nation’s financialcontrols appear to be made for the sole purpose of being evaded. Eventhe ability of central banks to regulate the supply of money and creditwas undermined by commercial banks’ borrowing and lending offshore.All national authorities were forced to scrap long-established interestrate ceilings such as regulation Q, lending limits, portfolio restrictions,reserve and liquidity requirements, and other regulatory paraphernalia.

In the United States, innovations proliferated rapidly in response tothese challenges. Money market funds appeared, investing in govern-ment and high-grade commercial paper and using the proceeds to payrates of return on “near-money” accounts which were high enough todraw deposits from banks. There was an upward shift in the wholestructure of interest rates. Another outcome was the saving and loan(S&L) crisis. With higher-deposit interest rates, the fixed-rate mortgage-based asset portfolio of the S&L system became unviable. With LLRsupport in the background, these institutions turned to heavy investmentin speculative assets like junk bonds and shopping malls, leading to aninevitable collapse.6

A further step was the formation of investment funds, in the firstinstance for “asset securitization,” expanding upon the activities ofFreddie Mac and Fannie Mae. Banks sold packages of assets to trustswhich in turn issued shares, with dividend payments passing through theinterest receipts to their equity-holders. In many cases the primary assetswere high risk (credit cards, car loans), but packaging them permitted re-duction of perceived risk through diversification. In effect, a new invest-ment vehicle was created, paying high returns.

Finally, novel high risk/high return packages were put together for in-vestors who inhabit that segment of the market. Innovations took theform of “derivatives” or complex contingent contracts based on under-lying securities. “Hedge funds” appeared to trade in derivatives, typi-cally financing their operations with heavy borrowing on the margin(with liabilities reaching ten times the value of their equity and more).Again, the outcome was more upward pressure on interest rates and in-creased financial instability worldwide (Eatwell and Taylor 2000).

As observed in Chapter 1 (note 12), these developments were associ-ated with a substantial increase in the ratio of borrowed funds to grosscapital formation for the U.S. nonfinancial corporate sector. As it turnedout, however, most of the extra resources were used to finance M&A ac-

264 chapter eight

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tivity (Pollin 1997). For the reasons just discussed, increased credit avail-ability was not associated with any downward trend in real borrowingcosts (insofar as such movements can be isolated from the actions of thecentral bank).

All this history is consistent with a Minskyan or structuralist interpre-tation of the financial system. Perhaps it fits less well with the more hy-draulic vision of the “accommodationist” Kaldor-Moore school, whichpostulates short-term endogeneity of the money supply via central bankor financial market ratification of commercial banks’ lending behavior.

3. Endogenous Money via Bank Lending

This section is devoted to a simple model of an endogenous money sup-ply, along accommodationist lines. It basically reworks the analysis inPalley (1996, chap. 7) in focusing on how money can be created in re-sponse to changes in the volume of loans in a fully specified Tobin-stylefinancial market model.

The intellectual background is Nicholas Kaldor’s crusade against Chi-cago monetarist analysis of the sort described in Chapter 6. Beginning inthe late 1950s with testimony to the (British) Radcliffe Committee on theWorking of the Monetary System and continuing until he died in 1986,Kaldor argued that under modern capitalism the central bank has littlechoice but to accommodate the lending activity of commercial banks,presumably at some stable rate of interest. A predetermined or exoge-nous money supply is the central dogma of monetarism; Kaldor hopedthat if it were shown to be unrealistic, the rest of that particular form ofanti-Keynesianism would disappear. Maybe so, but it is also fair to addthat Kaldor underestimated the desire of economists to adhere to Say’sLaw. If they can’t do it with exogenous money and the real balance ef-fect, there is always some other channel.7

Moreover, just saying that the central bank has the option to peg theinterest rate doesn’t alter the supply-driven causality of the monetaristmodel. In a standard money supply framework like the one sketched inequation (2) and fully developed in Chapter 4, the central bank can al-ways fix the nominal rate i by adjusting its holdings of T-bills Tc (thuschanging the level of nonborrowed reserves of commercial banks) or byaltering reserve requirements to shift the money multiplier ζ (essentiallythe inverse of the required reserve/deposit ratio). Despite the peggedrate, what the central bank chooses to do with high-powered moneydrives the system. Kaldor and successors such as Moore and other Amer-ican post-Keynesians want the driving force for money creation to be

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lending activity by commercial banks. The balance sheets in Table 8.1 setup a framework in which bank credit creation has some traction. Tokeep the analysis simple, a stable money multiplier is anachronisticallyassumed to exist.

Table 8.1 differs from the more conventional Table 4.2 in four impor-tant ways. First, equity with a value PvV is omitted from the accounting,because it is tangential to the present discussion. Absent asset prices suchas Pv that can jump discontinuously, net worth Ωh of business firms canonly change gradually over time as retained earnings accumulate. It isconstant in the short run.8 Net worth Ωh of households is similarly deter-mined by the accumulation of savings flows.

The second difference is that the business sector holds deposits Mf

such as CDs with commercial banks. The subscript reflects a “finance de-mand” for balances introduced by Keynes (1937b) in one of his manyfollow-up papers to The General Theory. He wrote that such balances“may be regarded as lying half-way so to speak, between active and inac-tive balances” (with active balances being used to satisfy transactions de-mands and inactive balances, liquidity and/or speculative demands formoney). The interpretation here is that Mf is held by productive firms asa revolving fund to support capital formation. When firms borrow morefrom banks to support higher investment, their loans Lf and deposits Mf

go up together, because Ωf cannot vary in the short run. The importanceof such transactions can be judged from Table 1.5. At the end of 1999,U.S. nonfinancial business had about $1.2 trillion in loans outstandingin the form of bank credit and held $900 billion of broad money, withboth numbers on the order of 10 percent of GDP. Households are alsoassumed to take loans Lh (think of credit cards) from the banks.

Third, loans “create money” along the lines of the causal chain in (4).Commercial banks have numerous options to obtain the correspondingrequired reserves. For simplicity, only one is built into Table 8.1. Thebanks can draw advances D from the central bank discount window

266 chapter eight

Table 8.1 Balance sheets for an “accommodationist” money supply.

Households Firms Commercial BanksMb Ωh qPK Lf H Mb

Ma Lh Mf Ωf L Mf

Th D

Central Bank Money Market GovernmentTc H Ta Ma TD

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at a specified interest rate id. Such borrowed reserves along with non-borrowed reserves Tc sum to H, the supply of high-powered (or base)money. Discount borrowing allows the banking system to expand itsloan supply while still respecting the reserve requirements that underliethe credit multiplier relationship Mb +Mf = ζH= ζ(Tc +D) with ζ > 1.9

Causality now runs from loans L to the money supply Mb + Mf =[ζ/(ζ − 1)]L, and back to base money H = L/(ζ − 1) and discount bor-rowing D = H − Tc.

Fourth, “money market funds” are assumed to exist, holding T-billsTa as an asset and offering near-money deposits Ma to households as thecorresponding liability. How this new sort of financial intermediary in-fluences the structure of interest rates is discussed in the following sec-tion. For the moment, we set Ta = Ma = 0.

Before we jump into the algebra, one last observation is that asset andliability choices are assumed to depend only on the directly relevant in-terest rates. In principle, all portfolio decisions should depend on all therates in the model (five in total), but in practice carrying a host of partialderivatives explicitly in the algebra just creates notational chaos in ex-change for negligible economic insight. So in what follows, demand andsupply functions for financial instruments are kept as simple as possible.

Two questions immediately arise: How does L get determined? Whydo households agree to hold the quantity of money Mb that banks chooseto provide them?

To answer the first query, let il be the interest rate on bank loans. It isnatural to assume that firms have a loan demand function such as

Lf = λ fd (il, gi)qPK, (5f)

in which gi stands for investment demand (scaled to the capital stock, asusual). The conventions are that ∂λ f

d /∂gi > 0 and ∂λ fd /∂il < 0, that is, de-

mand for loans (and finance balances Mf) rises with the level of invest-ment and falls when the loan interest rate rises. Total borrowing is scaledto the asset value of the capital stock.

Households’ borrowing is naturally scaled to their net worth,

Lh = λ hd (il)Ωh, (5h)

with a derivative d hdλ /dil < 0.

If the level of bank credit is proportional to their base of unborrowedreserves, then the loan supply function can be written as

Ls = λs(il, id)Tc, (6)

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with the first and second partial derivatives of λs being positive and nega-tive respectively.

Equilibrium in the loan market is determined by the condition that ex-cess demand equals zero,

Lh + Lf − Ls = 0, (7)

as illustrated in the upper quadrant of Figure 8.1. By the assumed signsof the partial derivatives of λ h

d , λ fd , and λs with respect to il, this equilib-

rium will be stable when the loan rate adjusts to clear the market.Households hold T-bills Th = T − Tc in an amount set by central bank

open market policy. Their holdings of money Mb and firms’ finance bal-ances Mf enter into an excess demand function for money of the form

Mb + Mf − [ζ/(ζ − 1)]L = 0, (8m)

while bond market equilibrium can be expressed as an excess supply re-lationship,

T − Tc − Th = 0. (8t)

268 chapter eight

T-bill interestrate it

Loan interestrate li

L Lh f+

Bank loansL

Ls

Figure 8.1Determination of vol-ume of bank lendingand interest rates inan accommodationistmodel of the bankingsystem.

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Households can be assumed to allocate their total financial re-sources—net worth plus loans—to money and bonds according to rela-tionships such as

Mb − µ(ib, it)(Ωh + Lh) = 0 (9)

and

Th − τ(ib, it)(Ωh + Lh) = 0, (10)

where ib and it are interest rates on bank deposits and T-bills respectively.Presumably, ∂µ/∂ib > 0 and ∂µ/∂it < 0 with the partials of τ having theopposite signs. Because households satisfy their balance sheet restrictionMb + Th = Ωh + Lh, the demand shares must sum to unity, µ + τ = 1.That is, only one of equations (9) and (10) is independent.

The model boils down to two equations. Plugging (5f), (5h), and (6)into (7) gives a loan supply-demand balance

λ hd (il)Ωh + λ f

d (il, gi)qPK − λs(il, id)Tc = 0, (11)

which solves for il as a function of gi. As already noted, the relevantschedules are in the upper quadrant of Figure 8.1. If the loan supplyfunction λs is elastic with respect to il (as shown), then higher investmentdemand will lead to only a small increase in the loan rate.

Substituting through the portfolio choice relationships and the bal-ance sheets in Table 8.1 reveals that just one of the two asset equilibriumconditions (8m) and (8t) is independent—if one of them clears then sowill the other. It is simpler to work with the one for T-bills, assumed toequilibrate via changes in it with ib held constant. The relevant equa-tion is

T − Tc − τ(ib, it)[1 + λ hd (il)]Ωh = 0. (12)

How (12) works is illustrated in the lower quadrant of Figure 8.1.Higher investment gi bids up credit supply and the loan rate il. At thesame time, the money supply increases through the credit multiplier.More expensive loans mean that households cut back their borrowingand reduce demand for bonds from (10). To ensure that they choose tohold the quantity of bonds supplied to them, Th = T − Tc, it must rise,with il adjusting to clear the credit market.10 Unsurprisingly, an increasein Tc via an open market bond purchase forces it to decline.

If, as shown, most of this financial adjustment takes place via quantitychanges, then we have a fair representation of the Banking School/Rob-ertson/Radcliffe Report/Kaldor vision of the monetary system in a modelwith a complete set of financial accounts. The keys to the results are the

structuralist finance and money 269

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elastic loan supply from the banking system and the willingness of thecentral bank to provide borrowed reserves without stint.

4. Money Market Funds and the Level of Interest Rates

The next step is to bring in money market accounts, as a financial inno-vation of a sort which along Schumpeterian lines cannot happen if “fullemployment” of financial claims is imposed at all times. In the small, for-malized world of Table 8.1, money market funds are the new idea. Theyare assumed to hold T-bills as assets, consolidating their running yield tooffer liquid near-money deposits at a rate ia close to that on governmentsecurities, say,

ia = it(1 − δ), (13)

with a “mark-down” rate δ not far from zero. With their good liquiditycharacteristics, the new deposits Ma can be assumed to be close substi-tutes with ordinary bank deposits Mb. Hence, if banks are to stay in busi-ness they will have to offer deposit interest at a rate ib not far from ia.Regulation Q has to go by the boards.

Moreover, banks will have negative cash flow unless it is true that

ilL > idD + ibMb, (14)

so that the loan interest rate il will be subject to upward pressure as ib

rises.11 As a major component of bank costs, the deposit rate ib will enteras an argument in the loan supply function λs in (6), with a negative par-tial derivative.

To work through detailed implications of the innovation, first notethat households now hold three assets—Ma, Mb, and Th—in their portfo-lios. The interest rate ia on money market deposits is linked to the T-billrate by (13). So there are two freely varying interest rates, ib and it, whichadjust to clear the markets for deposits and T-bills.

After substituting from the firms’ and households’ balance sheets, themoney market balance (8m) can be stated as

Ωf + [λ fd (il, gi) − 1]qPK + µ(ib, it)[1 + λ h

d (il)]Ωh

− [ζ/(ζ −1)]λs(il, ib)Tc = 0. (15)

Using the household balance sheet, the bond market equilibrium condi-tion is

T − Tc − [1 − µ(ib, it)][1 + λ hd (iI)]Ωh = 0. (16)

270 chapter eight

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With positive own-responses and negative cross-responses of house-hold asset demands to rates of return, equations (15) and (16) underlieFigure 8.2, in which a higher deposit rate bids up the T-bill rate in themarket for government paper, and a higher it bids up ib in the market fordeposits. (The dependence of the loan supply function λs on ib in (15)makes sure that the slopes of the two curves in the (it, ib) plane differ.)Such mutually positive feedbacks are characteristic of financial rates ofreturn. They will not destabilize the system so long as the effect of it on ib

is relatively weak and vice versa (the situation shown in the diagram).From (15), if loan supply λs shifts upward, then µ or the portfolio

share of deposits has to rise. The obvious mechanism is a higher depositrate, so the “Deposit equilibrium” schedule in Figure 8.2 moves upward.Bank credit creation is thereby associated with increases in both ib and it.

The system-wide analysis of Figure 8.1 has to be extended when themoney market enters the scene. In Figure 8.3, the loan rate il and stock ofbank credit L are determined in the northeast quadrant as before, exceptthat the intercept of the loan supply function Ls is assumed to shift up-ward with an increase in the deposit rate ib, as discussed above. Thislinkage creates a negative feedback from an increase in loan demand Ld

= Lh + Lf onto supply Ls. The impact effect of higher demand is to in-crease the deposit rate ib (southeast quadrant) via the mechanisms out-lined in Figure 8.2. But a higher ib in turn shifts up the loan supply sched-

structuralist finance and money 271

Interest rateon bankdeposits

ib

Interest rate onT-bills it

T-bill market

Depositequilibrium

Figure 8.2Effects of an increasein bank loans on thedeposits and T-billinterest rates.

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ule via the “Bank costs” curve in the northwest quadrant, choking offpart of the initial credit increase and bidding up il. Instead of shiftingfrom point A to B, the economy ends up in an inferior situation at C.

One implication is that the monetary system will be less accommoda-tive than in the post-Keynesian Figure 8.1. The invention of money mar-ket funds “closes the loop” in the left-hand quadrants of Figure 8.3, andhelps shift the whole interest rate structure upward. Asset owners nodoubt benefit, and in a Walrasian world there would be an overall gainin welfare from filling in a “missing market” for near-money deposits.But the real world is Keynesian, not Walrasian. It is not clear that thereare any gains in terms of progressive income redistribution and outputgrowth from creating a financial instrument that as its major impact bidsup the cost of finance for capital accumulation. As argued historically inEatwell and Taylor (2000), more arcane financial entities emerging in thewake of money market funds only strengthened these unhappy results.

5. Business Debt and Growth in a Post-Keynesian World

The foregoing is not the end of the story, of course. Endogenous moneyin the short run should lead along the lines of Chapter 7 into a theory of

272 chapter eight

Bank depositrate ib

Bank depositrate ib

Bank loaninterest rate

il

AB

C

45° Bank loansL

Ls

Ld

Bank costs

Figure 8.3Effects of an increasein loan demand onfinancial equilibrium.

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long-term growth. The literature in the area is scarce, but Lavoie andGodley (2000) set up a parsimonious model to address interesting ques-tions. A SAM and balance sheets appear in Tables 8.2 and 8.3.12

Table 8.3’s menu of financial claims is substantially reduced from theone in Table 8.1. There is a pure credit Wicksellian banking system withmoney held by households (M) as its liability and loans to firms (L) as itsasset. Wicksellian finance is a pretty good approximation of the freelylending and happily discounting commercial and central banks discussedabove. The predetermined real interest rate on both money and loans is j.Firms have zero net worth, and the asset value of their capital stock,qPK, is exhausted by their outstanding loans and the value of their eq-uity PvV. Capital is the only primary asset and households are the onlyactors with net worth Ω, so Ω = qPK. As will be seen, the natural statevariable for dynamic analysis is the debt/capital ratio λ = L/PK.

As usual the flow variables in Table 8.2 are also scaled to PK. To studyprocesses of accumulation, a good place to begin is with the flows offunds rows (E)–(G). Firms save a proportion sf of their income net ofinterest payments r − jλ (and transfer the rest to households as divi-dends δ = (1 − sf)(r − jλ) in cell B3). Their other sources of funds arenew borrowing λü and issuance of equity. A working hypothesis is thatthey finance a share χ of their capital formation with new shares, sothat PvÎ/PK = χg.13 With σf = sf(r − jλ), row (F) in the SAM can be re-stated as

sf(r − jλ) + λü − (1 − χ)g = 0. (17)

The post-Keynesian twist in this equation is the term for the growth ofbank credit, λü. The profit rate r and growth rate g are determined onthe real side of the model, so the supply of bank loans has to be endoge-nous to allow firms to carry through their investment plans.

Household consumption is assumed to depend on income and wealth,

γh = (1 − sh)ξh + φq,

using the fact that Ω = qPK. After substitutions from the row and col-umn balances in the SAM and the flow of funds for the banking system,the household flow of funds row (E) can be restated as

sh[(u − r) + (1 − sf)r + sfjλ] − φq − χg − λþ = 0, (18)

with the terms in brackets summing to σh. Because L = M and ü = þfrom the banking system’s balance sheet, accounting consistency ensuresthat households obligingly pick up the deposits that bank lendingcreates.

structuralist finance and money 273

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274 chapter eight

Tabl

e8.

2A

SAM

fora

post

-Key

nesi

angr

owth

mod

el(a

llva

riabl

essc

aled

byth

eva

lue

ofca

pita

lsto

ck).

Curr

ente

xpen

ditu

res

Chan

ges

incl

aim

s

Out

putc

osts

Hou

seho

lds

Firm

sBa

nks

Inve

stm

ent

Bank

asse

tsBa

nklia

bs.

Firm

s’eq

uity

Tota

ls(1

)(2

)(3

)(4

)(5

)(6

)(7

)(8

)(9

)

(A)O

utpu

tuse

sγ h

gu

Inco

mes

(B)H

ouse

hold

s(1−π

)uδ

jλξ h

(C)F

irms

πu

ξ f(D

)Ban

ksjλ

ξ bFl

ows

offu

nds

(E)H

ouse

hold

σ h−λ

$ M−

PV

PKv

. /0

(F)F

irms

σ f−

$ LP

VPK

v

. /0

(G)B

anks

−λ

$ Lλ

$ M0

(H)T

otal

su

ξ hξ f

ξ b0

00

0

Defi

nitio

nsλ=

L/PK

=M

/PK

δ=

(1−

s f)(

r−jλ

)

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The growth rate of the capital stock permitted by the available saving,gs, is the sum of (17) and (18),

gs = [sf(1 − sh)π + sh]u − sf(1 − sh)jλ − φq. (19)

Post-Keynesian investment functions of the sort estimated by Fazzariand Mott (1986–87) and Ndikumana (1999) emphasize cash-flow con-siderations. If the interest burden jλ increases, firms are likely to cut backon capital formation gi. For symmetry with the saving function (19) it isconvenient to make gi depend on q (as opposed to the profit rate r and in-terest rate j separately), and we also carry a term in capacity utilization:

gi = g0 + βu + ηq − ψjλ. (20)

The short-term macro equilibrium condition is gi − gs = 0, or

g0 + (η + φ)q + [sf(1 − sh) − ψ]jλ− [sf(1 − sh)π + sh − β]u = 0. (21)

The usual stability condition is a positive value for the term in bracketsmultiplying u in (21), sf(1 − sh)π + sh − β > 0. Assuming that it is satis-fied, note the ambiguous effect of jλ on u. A bigger debt burden reducesinvestment demand through the coefficient −ψ but also cuts into firms’saving. Filtered through profits distributed to households, lower retainedearnings create a net leakage reduction of sf(1 − sh)jλ. If this term ex-ceeds ψ, effective demand can be said to be “debt-led.” Otherwise, it is“debt-burdened.” The remaining term in (21) involves q. Through bothinvestment and saving effects, a higher q increases the level of economicactivity. How q itself gets determined is taken up below.

These distinctions become of interest in discussing the evolution of thedebt ratio λ. From the business sector’s flow of funds (17), its differentialequation can be written as

Ö = (sfj − g)λ + (1 − ψ)g − sfπu. (22)

Because firms typically don’t save 100 percent of their net profits πu −jλ, the growth rate versus interest rate criterion for the stability of λ dis-cussed in Chapter 6 is somewhat relaxed in (22). With sf < 1, j can ex-ceed g but the (partial) stability condition sfj − g < 0 can still be satis-

structuralist finance and money 275

Table 8.3 Balance sheets for a post-Keynesian growth model.

Households Firms BanksM Ω qPK L L MPvV PvV

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fied. There are also effects of λ on u and g to be considered. From thediscussion above and the reduced form direct dependence of g on u, theycan take either sign. To keep discussion of possible outcomes of themodel within limits, we assume overall stability, dÖ/dλ < 0.

By analogy to the stability analysis for ω in the (u, ω) plane presentedin Chapter 7, it is tempting to apply the same treatment to λ in the (u, λ)plane. Lavoie and Godley (2000) use the terminology “normal” for thecase in which dÖ/du < 0 via the coefficient −sfπ in (22). An increasein profits r = πu reduces the need of firms to borrow. The steady-statelocus along which Ö = 0 thereby has a negative slope. An alternative,“Minskyan” case arises through the terms in g in (22). If 1 − λ − ψ > 0(as is likely), then a strong effect of u on g through the investment func-tion could make dÖ/du > 0. The Ö = 0 locus would have a positive slope,with debt varying pro-cyclically as many of Minsky’s writings seem toimply.

The four stable configurations of the “Effective demand” and “Stabledebt” (or Ö = 0) schedules are shown in Figure 8.4.14 The upper two dia-grams depict the Lavoie-Godley normal case, and the lower two areMinskyan. Effective demand is debt-led in the northwest and southeast,and debt-burdened in the southwest and northeast. An immediate ques-tion is whether an expansionary shock (say, a reduction in the householdsaving rate) has effects that persist in the long run. The answer is that “it

276 chapter eight

B BA

C

BA

C

A

BA

C

C

Debtratioλ

Output/capitalratio u

Effectivedemand

Stabledebt

Effectivedemand

Stabledebt

Stabledebt

Stabledebt

Effectivedemand

Effectivedemand

Debtratioλ

Output/capitalratio u

Debtratioλ

Output/capitalratio u

Debtratioλ

Output/capitalratio u

Figure 8.4Long-run adjustmentin a post-Keynesian(Lavoie-Godley)growth model. Nor-mal and Minskyandiagrams (upper andlower); effective de-mand is debt-led inNW and SE; debt-burdened in SWand NE.

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depends.” For example, if the steady-state debt ratio rises with u (theMinsky case) and effective demand is debt-led, then as in the southeastdiagram, debt will grow faster than the capital stock after the initialshock, further increasing capacity utilization (and almost certainly thegrowth rate) as the economy moves from point A through B to C. A simi-lar scenario unfolds in the northeast if the steady-state debt ratio fallswith u and demand is debt-burdened.

The two diagrams to the left show more conventional cases (like theChapter 7 scenarios involving a profit squeeze in a profit-led economy)in which an initial positive demand shock generates responses tending topush u back down. The model behaves in Keynesian fashion in the shortrun, but is more classically inclined in the steady state (Duménil andLévy 1999).

Turning to the financial side of the model, households’ demands forthe two assets can be written as

µqPK − M = 0 (23)

and

νqPK − PvV = 0. (24)

Only one equation is independent, since µ + ν = 1 to make sure that thehousehold balance sheet really balances. The adjusting variable is the eq-uity price Pv, since M (= L) and V are given by history and the real inter-est rate is fixed. One can solve for Pv and q as

Pv = (ν/µ)(L/V) (25)

and

q = λ/µ. (26)

Suppose that liquidity preference declines, so that µ falls and ν rises.Then Pv and q necessarily go up. There is a positive demand shockin (21) from the higher valuation ratio, and u and λ set forth on one ofthe trajectories in Figure 8.4. This demand expansion is consistent withKeynes’s hints throughout The General Theory that high savers and bearspeculators with high liquidity preference (with members of both groupscoming from the same social class?) are the chief culprits behind laggingeffective demand.

In the present setup, the positive effect of falling liquidity preferenceon asset prices and q follows directly from the rudimentary financialspecification. However, similar results can be derived in the more com-plete market structure used in the previous sections, if it is extended to

structuralist finance and money 277

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include equity. Instead of an exogenously fixed interest rate, the key as-sumptions would be that commercial banks have elastic loan supplyfunctions and that the central bank stands ready to back up their lendingdecisions by creating reserves. These hypotheses may be appropriate formost advanced capital economies most of the time. But there are peri-ods—say in the United States after the interest rate hikes in 1979—whenthey clearly do not apply.

Finally, it would not be terribly difficult to extend the model to takeinto account households’ borrowing collateralized by their equity hold-ings. A reduction in the saving rate sh to make room for loans as a house-hold source of funds in (18) would give a demand kick, and also push themodel toward a debt-led configuration. If the southeast diagram in Fig-ure 8.4 applies, a substantial boom could result—the American case inthe 1990s? Of course a subsequent downswing accompanied by risingsaving rates and the threat of debt-deflation could be severe. A cyclicalextension of the present model is set out in Chapter 9 to analyze some ofthese issues.

6. New Keynesian Approaches to Financial Markets

New Keynesians have also taken an interest in financial fragility, in partbecause it provides a means to amplify productivity shocks into big eco-nomic fluctuations in extensions of the real business cycle models dis-cussed in Chapter 6. The same mechanisms can apply in the structural-ist cycle models discussed in Chapter 9. The new Keynesian leitmotif isthat higher net worth of enterprises is associated with more abundantcredit, lower risk of bankruptcy, and higher investment and growth.Since net worth increases in a cyclical upswing, a positive financial feed-back or accelerator mechanism is built into the system, analogous todebt-led growth in the southeast corner of Figure 8.4.

The popular models put great effort into providing formalized MIRAmicro foundations for their results, and it would take us too far afield tocrank up the machinery here. So a verbal sketch of two of the more im-portant research programs is all that follows. In terminology introducedin Chapter 4 and here, they respectively conflate lender’s risk and moralhazard, and borrower’s risk and adverse selection. The world of thesemodels is far from Modigliani and Miller’s because “asymmetric infor-mation” held by different participants in financial markets rules their be-havior, although the historical origins and sociological underpinnings ofthe asymmetries are things new Keynesians rarely discuss. And of coursethe models are all anti-Keynesian in that relevant probability distribu-

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tions and the capacity of “agents” to calculate around them are auto-matically assumed to exist.

In one of series of papers, Bernanke and Gertler (1990) consider a caseof moral hazard in which lenders and borrowers have the same knowl-edge about the probability of success of investment projects before theyare undertaken, but only the borrowers/investors know ex post howthey have worked out. This difference in knowledge creates a princi-pal/agent relationship between lenders and borrowers, in which the for-mer can set up some sort of monitoring apparatus to reduce their uncer-tainties about how well projects have succeeded. There is an “agencycost” associated with monitoring.

Bernanke and Gertler assume that agency costs decrease with firms’net worth. The cost of lender’s risk being lower, the supply of credit goesup, providing the positive feedback mentioned above. There are a coupleof significant macroeconomic implications. One is that the business cycleis not symmetric. Because net worth varies pro-cyclically, contractionsare sharper and shorter than expansions.

Second, there is redistribution of wealth between creditors and debt-ors over the cycle. Output contraction and (perhaps) price deflation shiftnet worth from borrowers to lenders, forcing the former to cut back oncapital formation. Bernanke and Gertler interpret this result as a formal-ization of Fisher’s (1933) views about debt deflation.

In a specimen from another series of papers, Greenwald and Stiglitz(1993) analyze a case of ex ante asymmetric information in which firmsissuing new equities know more than potential buyers about how theirinvestment projects will work out before they are undertaken. Firms relyon selling stock to finance their projects, but run the risk of bankruptcywith associated costs if they don’t succeed. If they have higher net worth,their bankruptcy costs are lower and their investment demand will bemore buoyant. We have much the same macro story as in Bernanke-Gertler, but the micro foundations are different.

Greenwald and Stiglitz present a cyclical story not dissimilar to that ofthe model of last section or scenarios of the sort presented in ChapterNine. In an upswing, an initial positive productivity shock leads bothprofits and real wages to rise. However, the labor market tightens andgrowth of net worth lags behind growth of the wage bill. Balance sheetsbecome weaker. A profit squeeze and increased bankruptcy risk cause adownturn, during which demand for labor weakens, setting up condi-tions for a recovery.

To quote Mishkin (1990), “A financial crisis is a disruption to finan-cial markets in which adverse selection and moral hazard problems be-

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come much worse, so that financial markets are unable to efficientlychannel funds to those who have the most productive investment oppor-tunities. As a result, a financial crisis can drive the economy away froman equilibrium with high output in which financial markets perform wellto one in which output declines sharply.”

Although new Keynesians perhaps overestimate the verisimilitude oftheir informationally asymmetric hobbyhorses as sources of cyclical os-cillations, Mishkin’s summary of historical financial disruptions is notfar off the mark.

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chapter nine

z

A Genus of Cycles

Although business cycles are always with us, constructing theories aboutthem has been an off-and-on avocation among economists. Samuelson’s(1939) multiplier-accelerator scenario was a landmark of early Keynes-ianism. But among his intellectual grandchildren, accelerators have dis-appeared from new Keynesian discourse, despite their apparent empiri-cal superiority to formulations based on Tobin’s q. Entrepreneur-drivencycles—whether linked to Schumpeter’s (1947) waves of creative de-struction and technical advance or to von Hayek’s (1931) overinvest-ment due to banks’ holding the interest rate below its natural level—have been supplanted on the Right by the real business cycle computableblack boxes discussed in Chapter 6. As also observed in that chapter,some Marxists have seen cycles as the result of “excessive” levels of in-vestment or capital per worker. Others emphasize distributive conflict,which was the basis for Goodwin’s (1967) predator-prey model of cycli-cal growth. Goodwin serves as a natural jumping-off point for extendingthe structuralist models of Chapters 7 and 8 to deal with cycles.

This chapter is devoted to a half-dozen simple cycle models that at-tempt to capture the essentials of several ideas about economic fluctua-tions. The formal specifications all boil down to sets of two differentialequations with a similar mathematical form—a genus of cycles. Con-sider the Jacobian J of the two equations evaluated at a stationary point:

Jj jj j

=

11 12

21 22, (1)

with Tr J = j11 + j22 and Det J = j11j22 − j12j21. We will be considering sys-tems in which the first variable has stable own dynamics, j11 < 0, whilethe second feeds back positively into itself, j22 > 0, creating a potentialinstability. If the system is to avoid a saddlepoint with Det J < 0 and in-stead generate cycles, it has to be damped by oppositely signed off-diago-nal entries, that is, j12j21 < 0. An increase in the second variable sets off aresponse in the first that drives the second back down.

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If the damping is strong enough, the differential equations will gener-ate a convergent spiral around the stationary point in a two-dimensionalphase diagram. Continuing exogenous “shocks” would be required tokeep the damped cycle going over time. The spiral may also tend towarda “limit cycle” around a “closed orbit,” or else it may diverge. In the fol-lowing discussion, we will not be greatly concerned with which possibleoutcome occurs. To find out, one has to resort to relatively sophisticatedmathematics which would take too much time to develop here.1 Rather,the emphasis will be on describing economic mechanisms that can makethe potentially destabilizing positive value of j22 and damping through j21

and j12 show up in the first place.In the models presented in this chapter, instabilities arise in three

ways—from distributional conflicts, destabilizing expectations, and a“confidence variable” that feeds back positively into itself. The Good-win model is first presented, in original and structuralist variants, fol-lowed by a model in which the real exchange rate is at the root of dis-tributive conflict. A monetary growth model initially set out by Tobinillustrates destabilizing expectations, and a multiplier-accelerator model,a Minsky-style model of cyclical finance, and a model of potential over-investment all are driven by confidence in one form or another. Twomore models are sketched in Chapter 10—a fiscal debt cycle involvingexpectations-driven exchange rate dynamics in advanced economies,and confidence-based fluctuations in capital inflows that can provokefinancial crises in capital-importing developing countries.

1. Goodwin’s Model

Richard Goodwin (1967) rather neatly arbitraged mathematical modelsof species competition worked out in the 1920s (Lotka 1925; Volterra1931) into economics, to set up a “predator-prey” scenario involvingdistributive conflict between capitalists and workers. The workers, as itturns out, are the predators with economic activity and employment asthe prey. A whole econometric literature on a cyclical profit squeeze fol-lowed in Goodwin’s wake. Representative papers include Desai (1973),Goldstein (1996), and Gordon (1997). A general finding is that profitsqueeze cycles exist for the U.S. economy. They are only slightly dampedand therefore are repetitive. Further supporting evidence is provided insections 2 and 3.

Goodwin assumed full utilization of capital and savings-determinedinvestment. Let K = κX, with κ as a “technologically determined” cap-ital/output ratio. The employed labor force is L = bX. If N is the to-tal population, then the employment ratio λ is given by λ = L/N =b(K/κ)/N. The growth rate of N is n. The wage share is ψ, and if all

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profits are saved the growth rate g of the capital stock becomes g = (1 −ψ)X/K = (1 − ψ)/κ.

Over time, the evolution of the employment ratio is determined bygrowth in output and population,

Ö = λ(g − n) = λ[(1 − ψ)/κ] − n. (2)

Along Phillips curve lines, the wage share is assumed to rise in responseto the employment ratio,

Ü = ψ(−A + Bλ). (3)

At a stationary point where Ö = Ü = 0, the Jacobian of (2)–(3) takesthe rather extreme form

J =−

00λ κ

βψ/

.

The two variables basically damp fluctuations in one another, with nointrinsic dynamics of their own. Hirsch and Smale (1974, p. 262) showthat with zeros along the diagonal of the Jacobian, λ and ψ chase eachother endlessly around a closed orbit in the (λ, ψ) plane which encirclesthe stationary point (λ*, ψ*). See Figure 9.1, in which the particular orbitthat the variables trace is set by initial conditions. The labor share is thepredator since it rises with λ. The employment ratio, in turn, is the preysince a higher value of ψ squeezes profits and cuts back accumulationand growth.

a genus of cycles 283

Employment ratioλ

λ*

ψ*

Wage shareψ

Figure 9.1Closed orbits in theGoodwin model.

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2. A Structuralist Goodwin Model

In slightly modified form, the structuralist macro model presented inChapter 7 generates Goodwin-style cycles.2 In the discussion to follow,we first concentrate on real wage and productivity dynamics on the sideof distribution and overall capacity utilization as an indicator of effec-tive demand. Subsequently we take up behavior of the nominal wageand price levels, and the components of demand.

To model the output cycle, we can treat capacity utilization u as a con-tinuously differentiable function of time. That is, instead of letting u =X/K jump discontinuously as in Figures 7.2, 7.4, 8.4, and so on, we nowassume that it varies according to the relationship

û = ¼ − ú. (4)

As will be seen, this “smoother” specification readily generates cycles,and is consistent with the relatively small changes quarter-by-quartertypically observed (for developed countries, at least) in macro time seriesfor aggregate demand and distribution.

Similarly, we have ψ = ω/ξ as the labor share, where ω = w/P is thereal wage and ξ = X/L is labor productivity. The analog to (4) is

Þ = Û − Õ. (5)

As in Chapter 7, we examine dynamics in the (u, ψ) plane. In growthrate form, the model can be restated in four equations:

¼ = α0 + αuu + αψψ, (6)

ú = β0 + βuu + βψψ, (7)

Û = γ0 + γuu + γψψ, (8)

and

Õ = δ0 + δuu + δψψ. (9)

If we set φi = αi − βi and θi = γi − δi, then substituting (6)–(7) into (4)and (8)–(9) into (5) gives reduced-form equations for u and ψ:

Í = u(φ0 + φuu + φψψ) (10)

and

Ü = ψ(θ0 + θuu + θψψ). (11)

What can we say about the signs of the coefficients in (10) and (11)?Beginning with equation (6), evidence presented in section 3 and else-

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where suggests that effective demand in the United States and other ad-vanced countries is profit-led, so that αψ < 0. There is a general consen-sus that the basic Keynesian stability condition ∂†/∂X < 0 is satisfied, orαu < 0. In (7), capital formation usually responds positively to both thelevel of economic activity and profitability, so that βu > 0 and βψ < 0. Itfollows immediately that φu < 0 so the differential equation (10) is lo-cally stable in u. Via the multiplier, the overall negative demand effect ofa higher value of ψ should outweigh its specific effect on investment, αψ> βψ, so that φψ < 0. In both diagrams in Figure 9.2, the “Effective de-mand” schedule along which Í = 0 has a negative slope dψ/du =−φu/φψ

in the (u, ψ) plane.The story about the “Distributive” curve along which Ü = 0 is tan-

gled. In the United States the real wage rises across cycles. During thecourse of one cycle, ω appears to respond more strongly than ξ tochanges in capacity utilization and the wage share, which itself variescounter to the capacity utilization cycle (see Figures 9.3–9.5 below). Theresulting pro-cyclical profit share is more likely to be observed if produc-tivity also moves pro-cyclically. Does this pattern hold?

In the relevant equation (9), δu will be positive if higher output inducesfaster productivity growth. The effect of ψ on ξ has to be interpretedalong cyclical lines. During a downswing in u, ψ tends to rise. A positivelagged response of ξ to ψ is then consistent with a rise in productivityduring and after the cyclical trough—the observed pattern. In summary,U.S. data suggests that both δu and δψ will be positive.

In equation (8) applied to the United States, the response coefficientsγu and γψ usually satisfy the relationships γu > δu > 0 and γψ > δψ > 0. Ahigher wage share appears to enhance labor’s bargaining power, as doesa higher level of capacity utilization. From the latter, we have θu = γu −δu > 0. One would also expect that θψ = γψ − δψ < 0. For the most partwith American data, this expectation is confirmed. However, during theperiod 1955–1970 the regression results reported below suggest that δψ<< 0, with productivity growth responding strongly to increases in theprofit share and making θψ > 0 so that dÜ/dψ > 0 as well.

This damped instability case is illustrated in the lower diagram of Fig-ure 9.2. For the determinant of the Jacobian to be positive, the Dis-tributive curve has to cross the Effective demand curve from above. Asshown, starting from a low point for u along the Effective demandschedule, the two variables follow a counterclockwise spiral around theequilibrium point—predator-prey dynamics again. The upper diagramcorresponds to θψ < 0, and represents a stable profit-squeeze of the sortemphasized by Boddy and Crotty (1975), Bowles, Gordon, and Weiss-kopf (1990), and the authors cited above.3 Both diagrams, of course,

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bear a close family resemblance to the ones in Figure 7.4. Their jumps inu have just been smoothed into cycles.

3. Evidence for the United States

Recall from the social accounting matrixes of Chapter 1 that there arenumerous payments flowing toward households in the U.S. economy.

286 chapter nine

Output/capitalratio u

Output/capitalratio u

Effectivedemand

Effectivedemand

Wage shareψ

Wage shareψ

Distributive

Distributive

Figure 9.2A structuralistGoodwin model, withstable (upper) andunstable (lower)wage sharedynamics.

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Just which should be called “wages” is by no means clear. A broaddefinition of labor payments incorporates wages and salaries paid sepa-rately by the private sector and the government, along with supplemen-tal labor income (social security, health insurance, and other benefits)paid by both. Government wages tend to vary against the capacity utili-zation cycle, have an upward oscillating trend between 1950 and 1970,and a downward trend thereafter. Supplemental labor income trends up-ward from 4 percent of the total in the 1950s to around 14 percent in themid-1990s with most of the growth prior to the mid-1980s. Wages paidby business vary pro-cyclically and the share has a slight downwardtrend through the early 1980s. On this definition, the real wage is weaklypro-cyclical in the sense that it picks up a positive response to u in regres-sion equations like those discussed below.

Figure 9.3 shows smoothed annual observations of the broadly de-fined labor share and capacity utilization in the U.S. economy from 1950through 2001. To scale u around a value of one, capacity utilization ismeasured relative to potential output calculated using CongressionalBudget Office (CBO) methodology as opposed to the capital stock.4 Thetrajectories in the figure broadly follow negatively inclined counterclock-wise spirals, with capacity utilization fluctuating by five to seven per-

a genus of cycles 287

64

66

68

70

72

74

93 95 97 99 101 103 105

1950

2001

Capacity utilization

Labo

rsh

are

Figure 9.3Capacity utilization and the broadly defined wage share in the U.S. economy, 1950–2001.

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centage points over a cycle, and the labor share by two or three points.There is an upward shift in the spirals in the late 1960s, due to the trendsin government wages and supplemental labor payments. Figure 9.4 pres-ents the longer history beginning in 1929. With much wider fluctuations,the same general pattern shows up in the earlier period as well. The sig-nificant exception is the decline in the labor share between 1944 and1950 as both capacity utilization and wages fell off from their wartimepeaks.

The cycles for the United States bear more than a passing resemblanceto the ones in Figure 9.2, which angle toward the southeast because thelevel of activity swings around the negatively sloped Effective demandcurve. It makes sense to explore econometrically how well an extendedversion of last section’s model applies to U.S. data.

For purposes of estimation, it is preferable to work with the laborshare of the business sector only, for at least two reasons. The series is re-liably stationary, because it does not incorporate the trending elementsof supplemental income and government wages. Second, price/quantitydata are not readily available for the nonbusiness sector. The labor shareis measured as an index number (1992 = 100), constructed from Bureauof Labor Statistics series on the business sector implicit price deflator,hourly wages, and product per hour. To impose a linear decompositionof ψ into its components, regression equations were run for ln ψ. More

288 chapter nine

Capacity utilization

Labo

rsh

are

58

60

62

64

66

68

70

72

74

80 85 90 95 100 105 110 115 120 125

1929

1933

19381944

1950

Figure 9.4Capacity utilization and the broadly defined wage share in the United States, 1929–2001.

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precisely, define f(ψt) = ln ψt − ln Ý, where ψt is the wage share at time tand Ý is its sample mean. For sample values close to the mean, we have

ln ψt − ln Ý ≈ f(Ý) + (1/Ý)(ψt − Ý) = (ψt/Ý) − 1.

There is an approximate linear relationship between ψ and ln ψ, whichin turn decomposes as ln ψ = ln w − ln P − ln ξ, parallel to the additivebreakdown of aggregate demand into its components presented below.

Capacity utilization is measured as the ratio of observed to potentialbusiness sector product in percentage points. Potential output is calcu-lated using the standard Hodrick-Prescott filter; results are much thesame on the CBO definition. For decomposition analysis, we can write ut

= ct + it + nt + gt at time t, with the four demand components being con-sumption ct, investment it, net exports nt, and government spending gt

measured relative to potential GDP. Implicitly, potential GDP and poten-tial business sector GDP are assumed to correlate closely, which they do.

Figure 9.5 presents annual data for capacity utilization and the la-bor share as just defined. A counterclockwise cycle persists in the (u, ψ)plane, beginning in 1947. Applying the Hodrick-Prescott filter to bothvariables suggests that movements in capacity utilization lead those ofthe labor share throughout most of the post–World War II period—pred-ator is led by prey. Measured in index number form, variations in ψslightly exceed those of u over cycles. Both series are stationary at the 1percent level of significance on Augmented Dickey-Fuller tests.

Dynamics of u and ln ψ were studied using an off-the-shelf vectorautoregressive (VAR) model of the form

y yt j t j

j

= + +−

=

∑φ Φ À t ,1

2

where yt = [lnψt ut] is a 2-by-1 vector containing the values of ln ψ and uat time t, f and Fj, j = 1, 2 are coefficient matrices of appropriate dimen-sions and, by construction, Àt is a vector of white-noise disturbances. Todefine the lag structure of the model, we set eight as the maximum lengthand computed Akaike information criteria for all specifications. The re-sults indicated that two is the best lag length.

Table 9.1 summarizes results of the VAR model for the period 1948–2001. The wage, price, and productivity variables (especially) increaseover time so all equations were estimated including trends. All coef-ficients were significant according to the standard tests, and the capacityutilization and labor share equations had adjusted R-squares of 0.75 and0.83 respectively. Through the lags, capacity utilization responds posi-

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tively to its own past values and negatively to the wage share. The equa-tion for u can be rewritten as

u − u(−1) = 36.01 + (1.24 − 1)u(−1) − 0.51u(−2)+ 0.28ψ(−1) −0.36ψ(−2)

so that ∆u = u − u(−1) has an overall negative response to the twolagged values of u.

In formal terms, the main stability criterion for an autoregressive (AR)model is that the sum of coefficients on “own” AR terms must be lessthan one. From Table 9.1, this requirement is satisfied for the u process:1.24− 0.51= 0.73< 1. Perhaps more intuitively, at a steady state it willbe true that u = u(−1) = u(−2), implying that u − u(−1) = 0, and ψ =ψ(−1) = ψ(−2). The implied slope of the steady-state effective demand

290 chapter nine

2001

1991

1971

1961

1951

19701982

1949

1975

1983

1958 1954

1976 19931992

19951998

1996

1997

19941999

19651977

19661989

19781955

19691962

1963

1964

1987

1974

19801957

1956

19591953

19481988

1981

1972196819901986

19671950 1985

2000

1952

1960

1947

19791973

1984

95

96

97

98

99

100

101

102

103

104

105La

bor

shar

eof

inco

me

95 96 97 98 99 100 101 102 103 104 105

Capacity utilization

Figure 9.5Scatter diagram of the labor share of income and capacity utilization in the U.S. business sector,1947–2001.

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curve is dψ/du = −(0.24 − 0.51)/(0.28 − 0.36) = −3.38 (or, as shownin the table, −3.46 when more significant digits are carried in the calcu-lation). Over the sample period, effective demand is profit-led, with aunit decrease in the index for the wage share resulting in a rise of aboutone-third of a point of capacity utilization.

The wage share responds positively to past values of capacity utiliza-tion and itself. The overall response of [ln ψ − ln ψ(−1)] to ln ψ(−1)and ln ψ(−2) is (−1 + 0.7 + 0.2) =−0.9, so the difference equation forln ψ is locally stable. The steady-state slope of the distributive curved(ln ψ)/d(ln u) is 2.02, signaling a profit squeeze.

Table 9.2 presents the slopes of the effective demand and distributivecurves for the Golden Age period and thereafter. A convenient break-point is the year 1970, which contained the trough of an NBER businesscycle. The initial year is alternatively 1948 or 1954 (the latter a troughyear which omits the immediate post–World War II and Korean War pe-riods).

Over both 1948–2001 and 1954–2001, demand is profit-led and there

a genus of cycles 291

Table 9.1 Estimated coefficients for capacity utilization and the labor share, 1948–2001.

const trend u(−1) u(−2) ψ(−1) ψ(−2) Steady state dψ/du

u 36.01 −0.00 1.24 −0.51 0.28 −0.36 −3.46c 53.06 0.02 0.39 −0.15 −0.09 −0.05I −13.62 0.00 0.86 −0.45 0.18 −0.30n 14.45 −0.01 −0.24 0.17 −0.18 0.12g −17.88 −0.01 0.22 −0.08 0.36 −0.12

lnu(−1) lnu(−2) lny(−1) lny(−2) Steady state d(ln ψ)/d(ln u)

ln ψ −1.34 0.00 0.04 0.16 0.70 0.20 2.02ln w 8.99 0.02 0.72 −0.60 1.15 0.53ln P 4.23 0.01 −0.49 0.26 −0.51 0.59ln ξ 6.10 0.01 1.17 −1.02 0.96 −0.27ln w/P 4.76 0.01 1.21 −0.86 1.66 −0.06

Table 9.2 Slopes of effective demand and distributive curves for subperiods,1948–2001.

Effective demanddψ/du

Distributived(ln ψ)/d(ln u)

1948–2001 −3.46 2.021954–2001 −3.24 2.111948–1970 −2.16 3.681954–1970 −1.58 −7.011971–2001 −8.01 1.23

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is a profit squeeze. Pre-1970, the demand effect is stronger (steady statedu/dψ is bigger in absolute value), and weakens during 1971–2001. Fur-ther sample splits suggest that demand may have shifted to being wage-led during the 1970s but was profit-led in the preceding and followingdecades.5 However, the number of observations per decade is too low tomake a solid case.

During 1954–1970, the distributive curve takes a negative slope andthe difference equation for ln ψ is locally unstable, as in the lower dia-gram of Figure 9.2. Along lines to be discussed below, the instability canbe traced to a vigorous productivity response to the profit share.

In sum, the qualitative characteristics of the economy are described bythe upper diagram in Figure 9.2. It follows that “permanent” distribu-tive shocks favorable to labor (upward shifts of the distributive curve)lead to an increase in the labor share at the expense of a reduction in ca-pacity utilization; and that positive demand shocks (upward shifts of thedemand curve) lead to increases in capacity utilization and the laborshare. Convergence around a “new” long-run intersection of the Effec-tive demand and Distributive curve will of course be cyclical.

Although the technicalities can safely be left to Barbosa-Filho andTaylor (2003), it is possible to use VAR estimation subject to adding-uprestrictions to express the demand components of u and the price/pro-ductivity components of ln ψ as functions of lagged values of these twovariables. The results of these reduced-form estimates are also shown inTable 9.1.

The estimated coefficients suggest that c, or the ratio of private con-sumption to potential GDP, has a positive trend and is pro-cyclical (oras we have seen in Chapter 1, the household financial surplus variescountercyclically). Investment i also varies pro-cyclically. Net exports nhave a downward trend and respond negatively to both capacity utiliza-tion and the wage share (interpreted as an index of labor costs). Govern-ment spending also has a negative trend, and responds positively to uand ψ. In the aggregate, the profit-led components predominate andthere is no overall trend in u.

Trends are stronger in the logs of w, P, and ξ. The coefficients are con-sistent with the descriptions above for the long period 1948–2001. Dur-ing 1954–1970, the sum of the coefficients on ln ψ in the productivityequation is −1.18, giving rise to the form of cyclical dynamics illustratedin the lower diagram of Figure 9.2.

4. A Contractionary Devaluation Cycle

The real wage or wage share is by no means the only object of distribu-tional conflict. In part because it affects the real wage, the real exchange

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rate ρ = e/P as analyzed in connection with Table 7.3 is often a bone ofcontention. (Recall that e is the nominal spot exchange rate and P is anational price level.) Its movements can set off cycles, especially whenreal devaluation has contractionary effects on output, apparently thecase historically in many developing countries. With a lag, devalua-tion may lead to an export push, followed by wage increases that cutback on exports and ultimately demand and real wages themselves. Fol-lowing Larrain and Sachs (1986) it is easy to model such interactionsover time.

As in Table 7.3, let À = E/K be the export/capital ratio. In equa-tion (28) in the table, À is assumed to respond immediately to a real de-valuation, or an increase in ρ. A lagged response is more realistic, for ex-ample,

Á = α[À*(ρ) − À], (12)

in which À*(ρ) is the “long-run” export level corresponding to a givenvalue of ρ. Because of preexisting contracts, the need to search for newforeign outlets, and so on, exports do not immediately respond to pricesignals. Rather, their foreign currency value À/e is likely to follow a “J-curve” (as a function of time) after a nominal devaluation, first droppingas e jumps up, and then gradually rising according to (12).

To keep the analysis conventional, suppose that there is a “natural”level Ä of the output/capital ratio at which wage inflation is zero. Moneywages may then change according to a simple Phillips curve,

¢ = βbw(u − Ä),

in which β is a response coefficient and b the labor/output ratio. Fromthis equation, a higher level of capacity utilization will make moneywages begin to rise, reducing the import cost ratio φ in equation (22) inTable 7.3. The real exchange rate also appreciates (moves downward),leading export expansion to slow.

Real exchange rate dynamics are given by

Ä = ρ(1 − φ)[ê − βb(u − Ä)], (13)

in which ê is an exogenous growth rate of the spot exchange rate. If de-valuation is contractionary, an increase in ρ pushes u down, making∂Ä/∂ρ > 0 and creating a potential instability.

Around a steady state with Á= Ä= 0 with positive À and ρ, the signs ofthe entries in the Jacobian of (12) and (13) are as follows:

ÀÁÄ

ρ− +− +

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The off-diagonal terms have offsetting signs and can stabilize the sys-tem. In contrast to the Goodwin models, now the “prey” variable hasunstable own-dynamics—instead of rapidly reproducing wage-sharefoxes, think of exchange rate rabbits.

Figure 9.6 illustrates the resulting cycles. The “Export response”curve corresponds to Á = 0 and the “Rate dynamics” to Ä = 0. Startingfrom an initial equilibrium, a maxi-devaluation followed by an exchangerate freeze displaces the real rate upwards. There is further depreciationuntil a trajectory crosses the Rate dynamics schedule. Because of the lagin the export response, À keeps growing until the spiral crosses thatcurve. A downswing follows, setting off a clockwise spiral with oscillat-ing exports and real exchange rate (not to mention output and inflation),or else cyclical divergence. A closed orbit would be an intermediate case.

An alternative policy could involve a steady depreciation at a rate ê.Via (13), this would shift the Rate dynamics schedule to the right, lead-ing to a long-term export gain but a lower real wage. If higher profitsand more exports stimulated technical advance, the economy couldjump to a higher growth path. Amsden (1989) suggests that elements ofsuch a strategy contributed to the South Korean export miracle aroundthe three-quarter mark of the twentieth century.

5. An Inflation Expectations Cycle

Talking about a Phillips curve already brings expectations into the pic-ture. Inflationary expectations, in particular, have been extensively ana-

294 chapter nine

Export/capitalratio À

Real exchangerate ρ Rate

dynamics

Exportresponse

Figure 9.6Contractionarydevaluationcycles.

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lyzed in a monetary growth model due to Tobin (1965). If adaptive ex-pectations about the change in the inflation are strong enough, they cancreate cyclical instability, with the expected inflation rate as the predatorand the real money stock per capita as the prey.6 The predator is the onewith unstable own-dynamics.

Tobin added simple fiscal and monetary accounts to Solow’s (1956)Say’s Law growth model (set up here in terms of the capital/labor ratio asopposed to its inverse as in Chapter 5). The government collects taxes Tfrom and makes transfers Z to the private sector, comprising N individu-als. If P is the price level, the real government deficit per capita is γg =[(Z − T)/P]/N. New money is created to finance the deficit, so that−γg + (/P)/N = 0 is the government’s flow of funds (government nega-tive real saving per capita is −γg). The per capita real money supply ism = (M/P)/N. If µ = þ is determined by fiscal policy, it will be true that(/P)/N = µm.

Output per capita is f(k), with k as the capital/labor ratio and f(k) aneoclassical aggregate production function in intensive form. Takinginto account transfers net of taxes that the private sector gets from thegovernment, its real disposable income per capita yRD is yRD = f(k) + γg.There is an ongoing inflation at an expected rate π. The private sectorknows how the (expected) inflation tax πm takes away real purchasingpower, and so has a perceived real disposable income per capita of yPD =f(k) + γg − πm = yRD − πm.

Real consumption per head, c, is set by the rule c = (1 − s)yPD.Per capita real saving σ thus becomes σ = yRD − c = s[f(k) + γg] +(1 − s)πm. If the population is growing at a rate n, total real investmentper capita is | + nk in standard fashion. Besides paying for investment,private sector saving is used to acquire the new money that the govern-ment deficit creates, so the sector’s flow of funds is σ − | − nk − µm =0. Combining these two expressions for σ and substituting for γg fromthe government’s flow of funds gives an expanded version of Solow’sgrowth equation | = sf(k) − nk,

| = sf(k) − nk + (1 − s)m(π − µ). (14)

The Mundell-Tobin assertion that faster expected inflation speeds upcapital formation is an immediate corollary. A higher value of π makesmoney a less desirable asset, so the private sector’s portfolio shifts inflow terms toward real accumulation.

As with the structuralist Goodwin model’s output/capital ratio inequation (4), it is convenient to assume that real money balances percapita change smoothly over time (that is, neither the money supply northe price level jumps),

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~ = m(µ − ¾ − n). (15)

A last step is to add a theory of inflation. In the literature around theTobin model, it has become conventional to postulate that the inflationrate responds to “excess money supply.” If for simplicity we stick to thequantity theory, then money demand MD is given by MDV = PK (wherethe Say’s Law assumption underlying the growth model means that de-mand can be scaled to the capital stock just as well as to output). Veloc-ity V is presumably an increasing function of the expected inflation rateπ: V′ = dV/dπ > 0. Real money demand per capita becomes mD =(MD/P)/N = k/V.

Fischer (1972) proposes that inflation dynamics be written down as

¾ = βp(m − mD) + π. (16)

That is, current inflation responds with a lag to money market disequi-librium and is also (somehow) influenced by the expected rate π.

Using (16) permits equation (15) for the change in real money bal-ances to be restated as

~ = mµ − βp[m − (k/V)] + π − n. (17)

If expectations about the inflation rate are formed adaptively, û= βπ(¾− π), then using (16) gives the differential equation

û = βπβPm − [k/V(π)]. (18)

Equations (14), (17), and (18) form a three-dimensional dynamic systemwith somewhat peculiar properties. Capital accumulation in (14) pre-sumably unfolds over years and decades. On the other hand, (17) saysthat the money supply expands smoothly, and in (18) it is hard to believethat expected inflation differs from the actual rate for any extended pe-riod of time.

In an extreme case, therefore, one could solve û = 0 in (18) for π,given values of k and m. This solution, together with the given k, couldbe used to solve for m with ~ = 0 in (17). These solutions would involvethe conditions π = ¾ = µ so that in the medium term (14) would revertto its basic Solow form. Sooner or later k would get close to an equilib-rium value k* with | = 0.

This sort of solution procedure is known as an “adiabatic approxima-tion” (Lorenz 1989). It basically says that the dynamics of a “slow” vari-able like k dominate the steady state of the system and that “fast” vari-ables like m and π are “slaved” to k. Such an approximation will notwork if the fast variables can act together in such a way as to destabilizethe system.

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In the present example, such an outcome depends on whether or not πand m can jointly generate an unstable predator-prey spiral. To try tofind out if they can, we can examine the Jacobian of the subsystem (17)–(18) at its equilibrium point, for some given value of k:

Jm m m V V

m V Vp p

D

p pD=

− − ′ −′

β β

β β β βπ π

[ ( / ) ]( / )

1.

Brute-force calculation shows that Det J = m and Tr J =βp[βπmD(V′/V) − m]. At an equilibrium point, it will be true that mD =m, so the condition for instability boils down to βπ(V′/V) > 1 orβπ(πV′/V) > π. The elasticity πV′/V is likely to lie between zero and one,so an inflation adjustment parameter βπ exceeding the rate of inflationcould set off a destabilizing spiral. An uptick in ~ would lead to higherreal balances and a positive û in (18), amplified by the positive feedbackin the southeast corner. A weak negative feedback in the northeast entrywould let ~ continue to be positive, and a destabilizing spiral would beunder way. According to (14), faster inflation would speed up growth. Itis difficult to believe that this happy situation would continue for verylong.7

6. Confidence and Multiplier

Expectations are of course unobservable. That fact of life can make em-pirical applications of models like the foregoing unconvincing. The samecriticism applies to investment functions of the sort proposed by Keynes,which explicitly incorporated shifting expectations over the cycle. De-spite this problem, it makes sense to try to think through how Keynesianinvestment (and saving) dynamics could work themselves out—the taskof this and the following two sections.

We begin with a simple exercise in which investment demand shiftsover time in response to a “confidence” variable ρ (redefined from beingthe real exchange rate) which feeds back positively into itself.8 Much thesame story underlies the many accelerator models proposed since thedays of Samuelson (1939).

The setup here replaces the static expectation function f(r) used in themodel underlying Joan Robinson’s banana in Figure 5.3 with the dynam-ics of ρ. The level of investment (per unit of capital) is gi, and the macrobalance condition is u = (1 − s)u + gi, so that from the usual multiplieralgebra we get u = gi/s.

A typical accelerator story has investment responding to the change inoutput (and thereby to the change in itself). To get to such a model via a

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confidence variable, we can assume in line with the specification of thebanana that the growth of investment depends on the difference betweenits expected return ρ and the profit rate r = πu (with π now standing forthe profit share instead of expected inflation) as an indicator of the costof capital,

Åi = g0 + α(ρ − πu) = g0 + α[ρ − (πgi/s)]. (19)

Positive feedback is added if confidence responds positively to itself.There is damping if ρ declines when the investment level is “too high,”

Ä = β(ρ − gi). (20)

The Jacobian for the system (19)–(20) takes the form,

Js

=−−

απ αβ β/

,

with Tr J = β − (απ/s) and Det J = αβ[1 − (π/s)]. For a positive determi-nant, the profit share has to be less than the aggregate saving rate. Inother words, households and/or the government as well as firms musthave visibly positive saving—the model might apply better to Japan thanto the United States!

In a phase diagram in the (gi, ρ) plane, the schedule corresponding tothe Ä = 0 condition would be the 45-degree line, and the Åi = 0 locuswould have a shallower slope (meaning that the base level of investmentdemand g0 must be positive). The configuration of the curves would bethe same as in Figure 9.6. An upward jump in confidence would kick offa clockwise spiral, unstable for a big β (highly responsive confidence)and/or a small α (unresponsive investment demand).

7. Minsky on Financial Cycles

This five-finger exercise becomes far more interesting when we bring inthe financial side of the economy. It turns out that changes in investors’confidence can lead to potentially destabilizing macroeconomic cycleseven when “the” interest rate is relatively stable in the face of aggregatedemand shocks. The text is Minsky’s (1975) book on Keynes, as partlyput into algebra by Taylor and O’Connell (1985). For simplicity, infla-tion as well as debt accumulation complications of the sort discussed to-ward the end of Chapter 8 (and in the following section) are ignored.

To focus attention on the stock market and Minsky’s interpretation ofthe valuation ratio q, we revert to supply-side determination of moneyand credit, as in the IS/LM model of Chapter 4. Balance sheets appear in

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Table 9.3, with both households and banks lending to business. Corpo-rate net worth Ωf is not restricted to zero and is treated as an endogenousvariable. The resulting degree of freedom will be filled by bringing inves-tor confidence into the picture as a factor determining q.

With government debt T held only by the banking system, the moneysupply rule is M = ζT, so that the supply of bank loans to firms is Lb =(ζ − 1)T. The economy-wide wealth balance is Ωh + Ωf = qPK + T.Given the shares ν and λ h

s of their wealth Ωh that households direct to-ward equity and loans to firms respectively, we can use their balancesheet identity to scale their net worth to the money supply,

Ωh = M/(1 − ν − λ hs ) = M/µ,

where µ (now) is the share of Ωh held as money. The loan market equilib-rium condition becomes

λdqZ − [(λ hs /µ)ζ + (ζ − 1)] = 0, (21)

where Z = PK/T is the capital/debt ratio to be used as a state variable formodel dynamics.

Minsky can be read as saying that the arguments of the loan demandfunction λd are the interest rate i and an expected profit rate re = r + ρ,where r is the observed rate of profit and ρ is an indicator of businessconfidence with a dimension consistent with that of r. The shares ofmoney and loans in household wealth (µ and λ h

s respectively) can be as-sumed to depend on i, re, and the output/capital ratio u as an indicator ofthe level of economic activity.

The expected profit rate re = r + ρ also determines the capital assetvaluation ratio q. Instead of emerging from the accounting as in Walras-Tobin models, q can reasonably be set equal to re capitalized by borrow-ing costs, that is q = (r + ρ)/i. When ρ is high and confidence is solid, theinvesting community ratifies its views by increasing its estimates of cor-porate wealth. From their balance sheet, the net worth of firms Ωf = qPK− Lh − Lb − PvV follows endogenously from the level of q and clearing

a genus of cycles 299

Table 9.3 Balance sheets for a Minsky-style financial instability model.

Households Firms Banking SystemM Ωh qPK Lh T MLh Lb Lb

PvV PvVΩf

GovernmentT

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of loan and equity markets. Evidently, with Ωf not restricted to zero,Minsky and Modigliani-Miller don’t mix.

For given levels of ζ and Z, excess demand for loans in (21) will be adecreasing function of the interest rate (when i goes up, λd will fall and λ h

s

will rise). An increase in the capital/debt ratio Z steps up demand forloans, thereby driving up i. Conversely, by raising loan supply, a higher ζmakes the interest rate go down.

Potential effects of changes in ρ (or r) on excess loan demand are moreinteresting. Minsky’s (1975) discussion rests squarely on Keynes’s ideathat liquidity preference is high when times are uncertain or simply bad.It follows that “during a boom the speculative demand for money de-creases” (p. 123, emphasis added). Further, on p. 76 if higher incomefrom a boom “is interpreted as increasing the surety of income from cap-ital-asset ownership, then the liquidity preference function will shift, sothat for a given quantity of money, the higher income, the higher the in-terest rate, and the higher the price of capital assets” (or the higher thevalue of q, in the notation utilized here).

The natural interpretation is that as economic activity and businessprofits rise, speculative demand for money goes down more than trans-actions demand goes up. This portfolio switch helps bid up equity pricesPv in that market’s equilibrium relationship,

(ν/µ)ζT − PvV = 0,

and increases the relative supply of loans. Excess loan demand in (21)becomes less sensitive to changes in actual and anticipated profit rates rand ρ so that the slope of the LM or “Loan market” curve in the (r, i)plane becomes more shallow at high levels of r. See Figure 9.7 for an il-lustration.9

If investment demand depends on q = (r + ρ)/i, then the IS or “Com-modity market” schedule determines macroeconomic equilibrium in Fig-ure 9.7. A higher confidence level shifts the loan market schedule up-ward and the commodity market curve to the right, leading to a newequilibrium with higher values of r and i. The shift in liquidity prefer-ence, however, means that the increase in i relative to r will be greater ata low initial profit rate (point A) than at a high one (point C). These con-trasting responses underlie Minsky’s cyclical dynamics.

To trace an oscillatory trajectory, we can begin by observing that thestate variable Z will evolve over time according to the rule10

‰ = Z(g − γgZ), (22)

where g is the rate of capital stock growth from the IS/LM system and γg

is the share of the fiscal deficit in the value of the capital stock. Because a

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higher value of Z raises the interest rate, ∂g/∂Z is likely to be negative;through both terms in parentheses we have ∂‰/∂Z < 0.

The other dynamic variable is of course the state of confidence ρ,which through positive feedback can generate cycles. A higher valuesteps up investment and the growth rate, so that ∂‰/∂ρ > 0. Changes in ρitself presumably depend on the general state of the economy. Con-fidence might increase, for example, when the actual profit rate r is highor the interest rate i is low. The analysis underlying Figure 9.7 suggeststhat changes in confidence should depend on the ratio of r to i (or on q as“normally” measured without the confidence term included in the nu-merator):

Ä = f(r/i), (23)

where f is an increasing function.Equations (22) and (23) can generate a clockwise cycle along the lines

discussed in sections 4 and 6. The system is potentially unstable, be-cause from Figure 9.7 a higher value of ρ can make the r/i ratio go up,that is, ∂Ä/∂ρ > 0. A higher Z raises the interest rate and reduces the levelof economic activity and enterprise profits, so that ∂Ä/∂Z < 0. The dy-namics are shown in Figure 9.8, for the possibly stable case in which thedeterminant of the Jacobian of (22)–(23) is positive. The “Confidence”schedule along which Ä = 0 must be steeper than the “Velocity” sched-ule for which ‰ = 0. The slope of the confidence curve is −fZ/fρ where

a genus of cycles 301

Interest ratei

Profit rater

A

D

C

B

Commoditymarket

Loan market

Figure 9.7Effects of an increasein investor con-fidence ρ on macro-economic equilib-rium at relatively low(A to B) and high (Cto D) levels of eco-nomic activity in theMinsky model.

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the subscripts stand for partial derivatives. The curve becomes flatterat high values of ρ because of the stronger effect of ρ on r/i shown inFigure 9.7.

A sudden loss of confidence at an initial steady state at A means that ρjumps downward to B. It then continues to fall, with Z also declining be-cause the interest rate is relatively high and investment drops off. Aftersome time, Z may fall enough to reduce pressure on loan markets and al-low the r/i ratio to start to rise (this transition will be quicker, insofar asthe strong effect of ρ on r/i weakens as confidence declines).

After the trajectory crosses the Confidence curve at C, ρ will begin torise, ultimately (at D) stimulating growth enough to permit ‰ to becomepositive. This upswing phase may last a considerable time, until the solu-tion trajectory crosses the flattened Confidence schedule at high valuesof Z and ρ. Depending on the strength of the positive feedback to con-fidence, the system may then oscillate back to A, orbit the steady stateforever, or diverge on a spiral path. The underlying real/financial interac-tions add a considerable degree of endogeneity to the cyclical process.

The swings in confidence underlying these events could be dampenedby central bank interventions. In the present model they would affect ρby shifting the interest rate through changes in the credit multiplier ζ.But if the authorities intervene to support confidence (which is by nomeans guaranteed), ρ itself may move upward over time, leading to in-creased moral hazard, more fragile financial positions, and the sorts ofchanges in financial structures discussed in Chapter 8.

302 chapter nine

Investmentconfidence

ρ

Confidence

Velocity

Capital/debtratio Z

A

D

C

B

Figure 9.8Dynamics of invest-ment confidence andthe capital/debt ratioin the Minsky model.

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8. Excess Capacity, Corporate Debt Burden, and aCold Douche

Sticking to the post-Keynesian theme of a stable interest rate, it is inter-esting to ask how animal spirits and corporate (as opposed to fiscal) debtinteract over the cycle. The Lavoie-Godley growth model presented inChapter 8 provides an arena for several questions:

Is there a tendency for industrialized economies to generate excess ca-pacity and/or a rising organic composition of capital, to prime theplumbing for a Schumpeterian “cold douche”?

If investment continues to rise while capacity utilization is falling,how does the implied “realization crisis” work itself out?

In particular, how long can investors’ optimism persist when overca-pacity begins to raise its head?

Such questions have been hotly debated in Left U.S. policy circles inrecent years, for example, in Greider (1997) and many subsequentpieces. They obviously cannot be fully answered by contemplating aclockwise spiral in a two-dimensional phase plane, but perhaps the con-struct to follow can shed some light.

Recall that the key state variable for Lavoie and Godley is λ, the ratioof corporate debt to the capital stock. One distinction implicit in theirmodel concerns the effect of λ on the output/capital ratio u. Is effectivedemand debt-burdened (∂u/∂λ < 0) or debt-led (∂u/∂λ > 0)? Second,if the debt ratio behaves in self-stabilizing fashion (dÖ/dλ < 0 in a totalderivative through the dynamic system), then what about the sign ofdÖ/du? Lavoie and Godley’s label for a negative value is “normal” as op-posed to a positive “Minskyan” response of debt growth to economicactivity.

To set up a cycle model around λ, we can bring in confidence. Thestraightforward approach is to make the intercept term g0 in the invest-ment function11 a dynamic variable,

Å0 = fg(λ, g0). (24)

Positive feedback can be introduced by making the second partial deriv-ative of the function fg positive; a degree of caution on the part of invest-ing firms (borrower’s and lender’s risks, and so on) suggests that the firstpartial should be negative.

It is simplest to treat u as a fast variable, slaved to g0 and λ. An in-crease in g0 raises effective demand, so the interactions have already beensketched in Figure 8.4. Given the signs of the partial derivatives of fg just

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postulated, the existence of a cyclical solution to (24) and the differentialequation for λ,

Ö = fλ(λ, g0), (25)

requires that dÖ/dg0 > 0, that is, a Minskyan debt growth response to ris-ing animal spirits.

Figure 9.9 shows the dynamics of (24) and (25), with the “Growth”schedule corresponding to Å0 = 0 and the “Debt” curve to Ö = 0. The fa-miliar clockwise spiral shows up.

An initial low-level temporary equilibrium at A will be associated witha falling debt burden and improving animal spirits until the (g0, λ) trajec-tory crosses the Debt schedule at B. Then λ begins to rise while g0 still in-creases until the Growth schedule is crossed (point D). Autonomous in-vestment begins to fall, and the cycle bottoms out as the debt ratiodeclines after the trajectory crosses the corresponding schedule again atE. Around that point, presumably, the cold shower kicks in.

What happens to capacity utilization while this spiral uncoils? Almostcertainly, u responds positively to g0. It is also likely that effective de-mand is debt-burdened. On these assumptions (∂u/∂g0 > 0 and ∂u/∂λ <0), we can sketch the positively sloped “Capacity utilization” contoursin Figure 9.9. Each curve shows combinations of g0 and λ that hold u

304 chapter nine

Corporate debtratio

Animal spiritsg0

Growth

Debt

A

DC

B E

Capacity utilizationcontours

Figure 9.9An animal spiritscycle in the Lavoie-Godley model.

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constant, with its level increasing across contours toward the southeast.On this accounting, a realization crisis occurs at point C, where the tra-jectory is tangent to a contour line. Thereafter, u falls while animal spir-its continue increasing until point D—growing overcapacity precedes afall in optimism in this scenario. Together with a rising debt burden, alower level of u slows investment demand; ultimately output X = uKwill begin to fall as well.

One argument in the late 1990s was that a cycle of the sort sketchedin the diagram was especially threatening because industrial capacityhad been growing worldwide since the mid-1980s under the stimulus ofglobalization. Instead of just one country’s macro system, the wholeworld’s was supposed to be going through a confidence squeeze. Appar-ent overinvestment in capital goods supporting information technology(excess capacity for computer components) and infrastructure for theInternet (thousands of miles of unused fiber optic cable) only made thesituation worse.

Second, inflation had slowed almost everywhere, so that fallingmarkup rates due to rising interest costs and decreasing capacity utiliza-tion were beginning to cause price levels to decline. Following Palley(1996) and the analysis in Chapter 8 it would be straightforward to adda more complete treatment of the financial system to the present setup toshow how debt-deflation could further cut into economic activity.

Third, wage increases as advocated by people on the Left cannot re-store aggregate demand if it in fact is profit-led. What is probably true isthat demand is not stimulated by higher interest rates. So attempts topush rates down make sense in terms of the present model. Whether sucha move would forestall massive worldwide output contraction combinedwith severe price deflation may still be an open question. As of mid-2003, hopes were still resting on a non-cyclical response of U.S. house-hold savings rates to the downswing, so that aggregate consumptioncould continue to hold effective demand high.

9. Final Thoughts

There are numerous oscillatory processes at work in the real econ-omy. Moreover, their import changes over time—recall the discussion inChapter 3 of the differences between nineteenth- and twentieth-centurybusiness cycles. Simple little two-dimensional models cannot begin tocope with all the fluctuations (and fluctuations of fluctuations) that exist.

Nevertheless, they can focus attention on key oscillations. Devalu-ation and (in Chapter 10) external debt cycles in developing econo-mies surely happen. In the United States, distributive and some sort of

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Lavoie/Godley/Minsky financial cycles are visibly present. (Inflation ex-pectation cycles probably are not that significant, despite their prolifera-tion in the mainstream literature.) Trying to put the whole set of motionsinto a plausible package is the challenge, which neither econometrics norcomputer simulation is likely to meet fully. But at least the toy modelsand their fancier cousins give a modicum of insight into some of themechanisms underlying the intrinsic fluctuations of capitalism. In the fu-ture, of course, new models will have to be developed to track novelforms of cycles when they inevitably begin to spiral.

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chapter ten

z

Exchange Rate Complications

Macroeconomics in a world in which two or more countries are open totrade, factor payments, and capital flows raises issues well beyond thosewe have discussed. A full structuralist treatment would require anotherwhole text. All we can do here is consider salient issues, mostly involvingdetermination of the exchange rate as the key “macro price” in an openeconomy. Some results to follow are controversial; they will be flagged aswe go along.1

As usual, we begin with accounting, and then go on to a series of ex-change rate models. In sequence, they attempt to determine the rate as anasset price, or as a consequence of commodity price arbitrage, or as anendogenous variable in a portfolio balance, flow-based Keynesian, ex-tended IS/LM, and a couple of monetarist macro models, or from othersorts of considerations (a more detailed preview of all these models ap-pears in section 2). After a quick detour to consider exchange rate-baseddebt dynamics in a developing-country context, the chapter closes withthe thought that although each model has serious problems on its ownterms, perhaps the set may serve to surround the beast. How well thefencing may work is the final topic.

A warning: the discussion jumps between levels of abstraction, inkeeping with the ways in which the different theories have been workedout. They all try to specify the “fundamentals” of exchange rate determi-nation. Another summary of the chapter is that for all practical purposesfundamentals do not exist—except when market participants convincethemselves that one or another of the many candidates truly matters.Once again, the beauty contest rules.

1. Accounting Conundrums

A central theme of this book is that often the best way to attack a prob-lem in economics is to make sure your accounting is right. Tables 10.1and 10.2 attempt this task for international trade and financial relations.

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Unfortunately, full accounting in models containing real and financialsectors for the “home” and “foreign” countries requires a wagonload ofsymbols. The details in both tables are needed to demonstrate the resultsthat follow. They follow broadly from a scheme proposed by Godley(1996).

Table 10.1 sets out flow accounts in the form of a SAM. Table 10.2presents the corresponding balance sheets. Since the emphasis is on ex-ternal transactions, economic actors in each country are aggregated intojust three groups—a private sector comprising households and nonfi-nancial business, government, and the banking system, which consoli-dates commercial and central banks. Variables referring to the home andforeign private sectors are labeled with subscripts h and f respectively.The foreign country’s stocks and flows are denoted by asterisks in bothtables.

As shown in Table 10.2, primary assets include capital stocks val-ued at their asset prices (qPK and q*P*K*) and outstanding short-termbonds or T-bills issued by the two governments (T and T*, with interestrates i and i* respectively). Both banking systems carry a subscript b, butthey are distinguished by their asset portfolios. The home system’s assetsare home bonds Tb and foreign bonds as reserves with a value eR*; the

308 chapter ten

Table 10.1 A Two-country SAM with trade and interest flows and international capital movements.

Current home expenditures Home ext. receipts Changes in home claimsExchange

conversions

Outputcosts Private Gov’t. Banks

Cap.form. Exports

Foreigninterest Money

Homebonds

For.bonds Totals

For. toHome

Home toFor.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Output (A) PC PG PI Pa*X* PXIncomesPrivate (B) V iTh Πb ei Th* * Yh

Gov’t. (C) τYh Yg

Banks (D) iTb ei*R* Yb

Flows of fundsPrivate (E) Sh −PI − &M −&Th −e &*Th 0Gov’t. (F) Sg

&T 0Banks (G) 0 &M −&Tb −eR&* 0ExternalImports (H) eP*aX eExports (I) −Pa*X* 1/eInt. in (J) −ei*Text* eInt. out (K) iText 1/eChange (L) −&Text 1/e

in ext. liab.Change (M) eText

&* ein ext. ass.

Totals (N) PX Yh Yg Yb 0 0 0 0 0 0

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foreign system holds foreign bonds Tb* and home bonds as reserves witha local value R/e. The banks have zero net worth and their liabilities arethe money supplies M and M* respectively. In their portfolios, the pri-vate sectors hold the relevant capital stock qPK or q*P*K*, both flavorsof bonds, and money M or M*. Unrealistically, the private sector in eachcountry is assumed to hold only the local currency. It is straightforwardto deal with the general case by using more symbols, but the SAM al-ready has too many.

Accounts for the home country appear to the left of the SAM, and forthe foreign country to the right. Cross-border flows are mediated by“Exchange conversions” between the two sides (the conversions also in-volve a sign change because an inflow to one country is an outflow fromthe other). The spot exchange rate, e, is the home currency price of for-eign currency.

Output and income generation relationships appear toward the north-west of each country’s part of the SAM. Real output levels are X and X*respectively, with prices P and P*. The corresponding costs of produc-tion are broken down in columns (1) and (1*). Total values of output PXand P*X* include payments for nominal value-added (V and V*) andimports (eP*aX and Pa*X*/e). As in other chapters, imports are treated

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Table 10.1 (continued)

Current foreign expenditures Foreign ext. receipts Changes in foreign claims

OutputCosts Private Gov’t. Banks

Cap.form. Exports

Homeinterest Money

For.bonds

Homebonds Totals

(1*) (2*) (3*) (4*) (5*) (6*) (7*) (8*) (9*) (10*) (11*)

P*C* P*G* P*I* P*aX P*X* (A*) OutputIncomes

V* i*Tf* Π g* iTf/e Yf* (B*) Privateτ∗Yf* Yg* (C*) Gov’t.

i*Tb* iR/e Yb* (D*) BanksFlows of funds

Sf* −P*I* − &M* −&*Tf −& /T ef 0 (E*) PrivateSg* &*T 0 (F*) Gov’t

0 &M* &*Tb − &/R e 0 (G*) BanksExternal

−P*aX (H*) ExportsPa*X*/e (I*) Imports

i*Text* (J*) Interest out−iText /e (K*) Interest in

& /T eext (L*) Changein ext. ass.

−Text* (M*) Changein ext. liab.

P*X* Yf* Yg* Yb* 0 0 0 0 0 0 (N*) Totals

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as components of cost.2 Real imports are scaled to outputs by coef-ficients a and a*, which could depend on relative prices such as the realexchange rate eP*/P in models of the neoclassical persuasion.

Rows (A) and (A*) show that outputs are used for the usual pur-poses—private consumption, government spending, investment, and ex-ports. For future reference, note how exports in cells (A6) and (A*6*)are valued at local prices. Rows (B)–(D) and (B*)–(D*) show how in-comes of the private sectors, governments, and banks are generated;their outlays and levels of saving appear in columns (2)–(4) and (2*)–(4*). In rows (B) and (B*), the private sectors receive incomes fromvalue-added and interest payments on their holdings of local and exter-nal bonds (for the home private sector, the receipts are iTh and ei*Th* re-spectively). The simplest way to deal with interest incomes on bank as-sets is to assume that they are passed along to the private sectors. In row(D), for example, the home banking system has interest income Yb = iTb

+ ei*R*. It transfers these returns Πb to the private sector in column (4):Πb = Yb. As a result of such maneuvers, savings of the banking systemsare equal to zero in cells (G4) and (G*4*). The governments get theirrevenues from taxes on private incomes (τYh and τ*Y*f ) in rows (C) and(C*).

Rows (E)–(G) and (E*)–(G*) show the different sectors’ flows offunds. As usual, “sources” of funds (saving and increases in liabilities)are positive and “uses” (increases in assets) are negative. The equationfor the home private sector in row (E),

Sh − PI − − £h − eTh& * = 0,

shows that it uses its saving Sh for capital formation PI and increasedholdings of home money , home bonds £h, and foreign bonds valued

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Table 10.2 Balance sheets for two countries.

Home Country

Private Sector Banking System GovernmentM Ω Tb M TTh eR*eTh*qPK

Foreign Country

Private Sector Banking System GovernmentM* Ω* Tb* M* T*Tf* R/eTf /eq*P*K*

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by the exchange rate eTh& *. Combined with differentiation of the home

household balance sheet in Table 10.2, this flow of funds equation givesthe change in nominal home private sector wealth as

ô = Sh + ÂTh* + (ÉP + q¯)K,

so that ô is the sum of saving and capital gains (or losses) from changingasset prices.

Row (F) shows that home government saving Sg must be negative if itis issuing a positive flow of new bonds (Sg = −£ < 0 when £ > 0). Inrow (G), the fact that the banking system’s saving has been set to zeromeans that the growth of the money supply responds solely to changes inbank assets, = £b + e¦*.

Three international payment flows go in each direction, for a total ofsix. See rows (H)–(M) and (H*)–(M*). In terms of their national prices,exports of the home and foreign countries (that is, foreign and home im-ports) take the values Pa*X* and P*aX in cells (A6) and (A*6*). Be-tween rows (I)–(I*) and (H*)–(H), home and foreign exports are con-verted to the other country’s prices by the inverse of the exchange rate(1/e) and its level (e) respectively (together with the sign switches men-tioned above) and then become imports in columns (1*) and (1).

Second, in column (7) the home private sector and banks hold foreignbonds in quantities Th* and R*. The values of their interest receipts inhome prices are ei*Th and ei*R*. With Text* = Th* + R* as home’s grossforeign assets, its total interest income is ei*Text* in cell (J7). After an ex-change conversion between rows (J) and (J*), the foreign government’sinterest payments in local prices on its bonds held abroad count as afiscal outlay i*Text* in cell (J*3*). The home government’s interest pay-ments on its gross external liabilities Text = Tf + R are treated analo-gously in column (7*), rows (K*)–(K), and column (3).

Finally, foreign asset holdings change over time, for example, £ext =£f + ¦ is the equation for foreign accumulation of the home govern-ment’s bonds at home prices. The exchange conversion is between rows(L) and (L*), and column (10*) gives bond accumulation in foreign prices.

The transactions appearing in the SAM correspond to the usual cate-gories in balance of payments accounts: trade in goods and services, fac-tor payments, and movements of capital. In a formal model, the tradeflows would be driven by activity levels and relative prices, and interestrates would adjust to make sure that asset markets (incorporating bothforeign and home flows) clear. Interest rates on asset stocks would set thelevels of factor payments.

As Godley (1996) emphasizes, an apparent puzzle in the SAM is thefact that while it includes numerous international transactions, there is

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no “balance of payments” per se. It is not obvious why all the cross-bor-der flows with their exchange conversions should add up to some over-riding “balance,” especially since all have their own separate determi-nants.

But the standard accounting does make sense. To see why, it is helpfulto think in terms of net foreign assets (NFA) N of the home country,which can be defined as

N = e(Th* + R*) − (Tf + R) = eText& * − Text, (1)

or (in the present example) home’s holdings of foreign bonds valued atthe spot exchange rate minus the value of its own bonds held abroad. In(1) it is clear that N follows from historically given gross asset and liabil-ity positions in that its level is set by the home economy’s history of cur-rent account deficits and surpluses and the ways in which they werefinanced. It is shown below that net foreign assets cannot “jump” in un-constrained fashion in temporary equilibrium—any change in the levelof gross assets has to be met by an equal change in gross liabilities tohold N unchanged. In this way, (1) becomes a binding constraint onmacroeconomic adjustment.

Net foreign assets can take either sign (including holdings of equity,they were about −$2 trillion for the United States as of 2002). As nomi-nal magnitudes, N and its foreign counterpart −N/e are subject to cap-ital gains and losses due to movements in the exchange rate. These arediscussed below, so for the moment we concentrate on quantity changesin N. Summing and substitutions among the rows and columns of theSAM give the following chain of equalities:

Sh + Sg − PI = e( & *Th + ¦*) − (£f + ¦) = Ç

=[Pa*X* + ei*(Th* + R*)] − [eP*aX + i(Tf + R)] = −Sf (2)

where Sf stands for the home country’s “foreign saving” or current ac-count deficit (if the home country is saving less than it invests, then therest of the world must be providing saving to make up the shortfall).

In the first line of (2) the sum of domestic sources of saving minus in-vestment is equal to the increase in net foreign assets. In turn, in the sec-ond line Ç is equal to the surplus on current account (trade plus factorpayments) or −Sf. All presentations of an economy’s “balance of pay-ments” are rearrangements of equations like those in (2). What they arebasically saying is that (apart from capital gains and losses), net foreignassets evolve over time in response to the current account. Decisionsabout how net assets are “stored” in terms of national portfolio alloca-

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tions (including amounts held in the form of international reserves) arediscussed below.

2. Determining Exchange Rates

Exchange rate regimes come in two basic varieties—fixed and floating.A “fixed” exchange rate sets a value for the local currency in terms of

the currency of some other country (or a weighted average of othercountries, if a “basket peg” is adopted). As a variation on the fixedtheme, the rate may be allowed to fluctuate within a band, or be revisedfrom time to time to guide its “real” value eP*/P in a certain direction.One such scheme is a “crawling peg” in which small, frequent exchangerate changes are used to offset a differential between inflation rates in thehome country and the rest of the world. Such a policy was examined interms of the contractionary devaluation cycle discussed in Chapter 9.

Since the market in which currencies are bought and sold never closes,a fixed value of the exchange rate must be maintained by interventions inthe market, typically undertaken by the home country central bank. Ex-amples include spot and forward sales or purchases of reserves, or inter-est rate adjustments, which attempt to change the dynamics of exchangerate movements over time. Market players may support or attack a fixedrate by buying or selling spot or forward assets denominated in the homecurrency, but that does not mean that the rate will change. Rather, forreasons discussed below, the country concerned will accumulate or losereserves. This will have further implications down the line.

Many developing countries pursue fixed-rate schemes of one form oranother. The sustainability of the rate today or tomorrow depends, as weshall see, on players’ perceptions of the economy’s “fundamentals.” Inthe wake of massive reserve losses in their crises of the late 1990s, Mex-ico, some East Asian countries, Russia, and Brazil adopted floating rates.How closely they will be managed or removed from immediate marketpressure by capital controls remains to be seen.

Since the early 1970s the developed countries have floated their ex-change rates, managed with greater or lesser concern by the authorities.At the end of the century, the major floating currencies were the dollar,the yen, the euro, and the pound sterling. Since the mid-1970s the UnitedStates has not been greatly concerned with the real value of its exchangerate and so comes closest to having a “pure” floating regime. But otherrich countries, including “Euroland” or the eleven nations initially ad-hering to the euro, are not far behind.

One standard line of argument about the determination of floatingrates is based on arbitrage in financial and/or commodity markets. A sec-

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ond focuses on stock and flow relationships involving asset portfoliosand macro balances as in Tables 10.1 and 10.2. Finally, more institution-ally oriented approaches attempt to pinpoint fundamentals that alleg-edly determine where the exchange market is likely to go.

Intertemporal forex arbitrage was analyzed in the 1920s by Keynes(1923), among others. It gives a rule known as “uncovered interest rateparity” (or UIP) by which the exchange rate can be calculated as an assetprice from expected changes in its value over time. UIP is intrinsically dy-namic, because it is based on arbitrage of own rates of return over time.

Also in the 1920s, the Swedish economist Gustav Cassell (1922) re-popularized an old exchange rate rule known as “purchasing powerparity” (or PPP) based upon current arbitrage in commodity markets.Exchange rates should be such that tradable commodities commandthe same prices in any country. Neither parity condition is observed inpractice, rendering their underlying assumptions somewhat dubious. Butboth are commonly used to calculate exchange rate fundamentals. If oneor the other of the hypotheses is badly violated, the market may con-clude that the current exchange rate is at an inappropriate level.

Macro-level theories concentrate on the exchange rate’s linkages withaggregates such as the trade balance, the composition of asset portfolios,or the overall balance of payments. If the rate is allowed to “float” orchange freely, it is supposed to arrive at a level that “clears” macro bal-ances. With the rate fixed, the balances may not achieve equilibrium inwell-determined ways.

The macro relationships that must be considered in the contemporaryworld relate to both the current and the capital accounts. Before and inthe first decades after World War II, it made sense to concentrate onlyon the trade account. A model proposed forty-odd years ago by Salter(1959) and Swan (1960) does contain a plausible exchange rate funda-mental—the traded/nontraded goods price ratio. At least as far as tradeis concerned, the exchange rate can be interpreted as becoming increas-ingly overvalued when this internal price ratio falls. But for the industri-alized countries at least, payments related to trade are now such a tinyshare of total external transactions that the model is obsolete (Eatwelland Taylor 2000).3

The two widely accepted Keynesian models incorporating the finan-cial side of the balance of payments date from the 1960s and 1970s.4 Theyounger concentrates on “portfolio balances,” and claims that the ex-change rate along with the two bond interest rates is determined by equi-librium conditions in three of four relevant financial markets—for homeand foreign moneys M and M* and bonds T and T* (the fourth market issupposed to clear by Walras’s Law). It is shown below that this claim is

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incorrect because there is just one independently clearing asset market ineach country.

The other model is usually attributed to Mundell (1963b) and Fleming(1962). In an open economy described by a 3 × 3 system of equations,adjustment dynamics are based on the ideas that the output level re-sponds to excess commodity demand from an IS relationship and the in-terest rate shifts in response to asset market imbalances in an LM. Thefloating rate is supposed to adjust when the balance of payments (or BP)does not clear. On the other hand, if the exchange rate is pegged then in-ternational reserves have to be the adjusting variable, making monetarypolicy endogenous. Solving all three equations simultaneously under thefixed or floating rate assumption gives the usual stability and compara-tive static results.

The Mundell-Fleming “duality” between reserves and the exchangerate evidently presupposes that a balance of payments exists, with a po-tential disequilibrium that has to be cleared. But as we have already seenin connection with Tables 10.1 and 10.2, the balance of payments is atmost an accumulation rule for net foreign assets and has no independentstatus as an equilibrium condition—an argument spelled out in detail be-low. The Mundell-Fleming duality is irrelevant, and in temporary equi-librium the exchange rate does not depend on how a country operates itsmonetary (especially international reserve) policy.

The bottom line assessment of the portfolio balance and Mundell-Fleming models is that they are not satisfactory approaches to exchangerate determination. In contemporary markets it appears that the rate isextrinsic to macro equilibrium as it emerges from adjustments in vari-ables such as interest rates or the general level of economic activity. Afloating exchange rate is not a “price” that equilibrates markets—apart,perhaps, from the markets in which its own future values are set via UIPor other intertemporal behavioral practices.

Evidently dynamic considerations have to brought in. Although itdoes not fit the data (Blecker 2002b), UIP is the obvious intertemporalmodel to consider. A formulation incorporating IS, LM, and UIP is pre-sented in section 8. It generates cyclical dynamics, as opposed to thesaddlepath jumps characteristic of more recently popular dynamic opti-mization models discussed in earlier chapters.

A further strand of the exchange rate story is a monetary approach tothe balance of payments worked out in the 1950s and 1960s (the reac-tion raging against Keynesianism at the time extended itself vigorouslyin the open economy direction). A sketch is given in section 9. There isalso a discussion of econometric attempts to specify fundamental causesof exchange rate changes, largely along monetarist lines. They all failed

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dismally. Finally the monetarist approach led into a well-known modelof exchange rate dynamics by Dornbusch (1976). It is outlined in sec-tion 10.

Two other analyses of the behavior of exchange rates are worth men-tioning. First, “twin deficit” models assume that the balance on externalaccounts is determined by the fiscal balance, which immediately emergesas another fundamental. In particular, deterioration in the external posi-tion is attributed to growing fiscal deficit. Second, the so-called trilemmasuggests that its three component policies—liberal capital markets, afixed exchange rate, and an independent monetary (or indeed, fiscal)policy—may be mutually incompatible. Because the Mundell-Flemingduality principle is invalid, it is argued below that the trilemma per semakes no sense. But it still is of some use in underlining the fact that thestate of expectations in the market is the exchange rate’s ultimate arbiter.

3. Asset Prices, Expectations, and Exchange Rates

Recall from Chapter 4 the definition of an own-rate of return to an assetas i = (Rexp/V) − c, that is, the net expected income flow (Rexp) per unitvalue of the asset (V) minus the carrying cost (c). Keynes thought that as-set prices like V “should” adjust to bring revenue streams net of carryingcosts into broad alignment with one another and with “the” interest rateas well. The quotation marks are meant to call attention to the fact thatarbitrage very often fails (in part for reasons he advanced in his beautycontest). Fully arbitraged asset prices represent a center of gravitation inthe market that is often honored in the breach.

The exchange rate becomes an asset price when it responds to poten-tial capital gains or losses in forward markets. Consider a Japanese in-vestor who wants dollars in one month’s time. He or she has two basicoptions. The first is to buy dollars now at the spot exchange rate e andhold them at the American (monthly) interest rate i. The total dollarsavailable at the end of the month will be e(1 + i). The alternative is tohold resources in yen at an interest rate i* and then buy dollars at theexpected forward rate f = e + À where À is the expected change inthe dollar/yen exchange rate. The total at hand after a month would bef(